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All Textbook Solutions for Precalculus

60PE For Exercises 57-62, find and simplify fx+h. (See Example 6) fx=x3+2x5 62PE 63PE 64PE For Exercises 63-70, refer to the function f=2,3,9,7,3,4,1,6. Determinef3.For Exercises 63-70, refer to the function f=2,3,9,7,3,4,1,6. Determinef2.For Exercises 63-70, refer to the function f=2,3,9,7,3,4,1,6. Forwhatvalueofxisfx=6?68PE 69PE For Exercises 63-70, refer to the function f=2,3,9,7,3,4,1,6. Forwhatvalueofxisfx=4?71PE Frank needs to drive 250 mi from Daytona Beach to Miami. After having driven x miles, the distance remaining rx (in mi) is given by rx=250x. a. Evaluate r50 and interpret the meaning. b. Determine the distance remaining after 122 mi.At a restaurant, if a party has eight or more people, the gratuity is automatically added to the bill. If x is the cost of the meal, then the total bill Cx with an 18 gratuity and a 6 sales tax is given by: Cx=x+0.06x+0.18x. Evaluate C225 and interpret the meaning in the context of this problem.A bookstore marks up the price of a book by 40 of the cost from the publisher. Therefore, the bookstoreâ€™s price to the student, Pxin$ after a 7.5 sales tax, is given by Px=1.075x+0.40x, where x is the cost of the book from the publisher. Evaluate P60 and interpret the meaning in the context of this problem.75PE For Exercises 75-84, determine the x-andy-intercepts for the given function. (See Example 7) gx=3x12 77PE For Exercises 75-84, determine the x-andy-intercepts for the given function. (See Example 7) kx=x+2 For Exercises 75-84, determine the x-andy-intercepts for the given function. (See Example 7) px=x2+12 80PE For Exercises 75-84, determine the x-andy-intercepts for the given function. (See Example 7) rx=x8 For Exercises 75-84, determine the x-andy-intercepts for the given function. (See Example 7) sx=x+3 83PE For Exercises 75-84, determine the x-andy-intercepts for the given function. (See Example 7) gx=x+3 85PE The amount spent on video games per person in the United States has been increasing 2006. The function defined by fx=9.4x+35.7 represents the amount spent fxin$x years since 2006. Determine the y-intercepts and interpret its meaning in context.For Exercises 87-96, determine the domain and range of the function. (See Example 8)For Exercises 87-96, determine the domain and range of the function. (See Example 8)For Exercises 87-96, determine the domain and range of the function. (See Example 8)For Exercises 87-96, determine the domain and range of the function. (See Example 8)91PE For Exercises 87-96, determine the domain and range of the function. (See Example 8)For Exercises 87-96, determine the domain and range of the function. (See Example 8)For Exercises 87-96, determine the domain and range of the function. (See Example 8)95PE For Exercises 87-96, determine the domain and range of the function. (See Example 8)For Exercises 97-110, write the domain in interval notation. (See Example 9) a.fx=x3x4b.gx=x3x24c.hx=x3x2+4 For Exercises 97-110, write the domain in interval notation. (See Example 9) a.kx=x+6x2b.jx=x+6x2+2c.px=x+6x22 For Exercises 97-110, write the domain in interval notation. (See Example 9) a.ax=x+9b.bx=9xc.cx=1x+9 For Exercises 97-110, write the domain in interval notation. (See Example 9) a.yt=16tb.wt=t16c.zt=116t For Exercises 97-110, write the domain in interval notation. (See Example 9) a.ft=t53b.gt=5t3c.ht=1t53 102PE For Exercises 97-110, write the domain in interval notation. (See Example 9) a.fx=x23x28b.gx=x+2=x23x28c.hx==x23x28x+2 For Exercises 97-110, write the domain in interval notation. (See Example 9) a.rx=x24x12b.sx=x24x12x+1c.tx=x+1x24x12 For Exercises 97-110, write the domain in interval notation. (See Example 9) a.wx=x+1+4b.yx=xx+1+4c.zx=xx+14 For Exercises 97-110, write the domain in interval notation. (See Example 9) a.fa=8a2b.ga=58a2c.ha=58+a2 For Exercises 97-110, write the domain in interval notation. (See Example 9) a.fx=x+15b.gx=x+152c.kx=5x+152 108PE For Exercises 97-110, write the domain in interval notation. (See Example 9) a.px=2x+1b.qx=2x+1;x0c.rx=2x+1;0x7 110PE For Exercises 111-114, use the graph of y=fx to answer the following. (See Example 10) a.Determinef2.b.Determinef3.c.Findallxforwhichfx=1.d.Findallxforwhichfx=4.e.Determinethex-intercepts.f.Determinethey-intercept.g.Determinethedomainoff.h.Determinetherangeoff For Exercises 111-114, use the graph of y=fx to answer the following. (See Example 10) a.Determinef2.b.Determinef3.c.Findallxforwhichfx=1.d.Findallxforwhichfx=4.e.Determinethex-intercepts.f.Determinethey-intercept.g.Determinethedomainoff.h.Determinetherangeoff 113PE 114PE For Exercises 115-122, write a function that represents the given statement. Suppose that a phone card has 400 min. Write a relationship that represents the number of minutes remaining rx as a function of the number of minutes already used x .For Exercises 115-122, write a function that represents the given statement. Suppose that a roll of wire has 200 ft. Write a relationship that represents the amount of wire remaining wx as a function of the number of feet of wire x already used.117PE 118PE For Exercises 115-122, write a function that represents the given statement. Two adjacent angles form a right angle. If the measure of one angle is x degrees, write a relationship representing the measure of the other angle Cx as a function of x .For Exercises 115-122, write a function that represents the given statement. Two adjacent angles form a straight angle 180. If the measure of one angle is x degrees, write a relationship representing the measure of the other angle Sx as a function of x .121PE For Exercises 115-122, write a function that represents the given statement. Write a relationship for a function whose fx values are 3 more than the principal square root of x .If two points align vertically then the points do not define y as a function of x . Explain why.124PE Given a square with sides of length s, diagonal of length d, perimeter P, and area A. a.WritePasafunctionofs.b.WriteAasafunctionofs.c.WriteAasafunctionofP.d.WritePasafunctionofA.e.Writedasafunctionofs.f.Writesasafunctionofd.g.WritePasafunctionofd.h.WriteAasafunctionofd.Given a circle with radius r, diameter d, circumference C, and area A. a.WriteCasafunctionofr.b.WriteAasafunctionofr.c.Writerasafunctionofd.d.Writedasafunctionofr.e.WriteCasafunctionofd.f.WriteAasafunctionofd.g.WriteAasafunctionofC.h.WriteCasafunctionofA.Graph the line represented by each equation. a.4x+2y=2b.y=1c.3x=12 2SP 3SP Given 2x+4y=8, a. Write the equation in slope-intercept form. b. Determine the slope and y-intercept. c. Graph the line by using slope and y-intercept.5SP Refer to the graph in Example 6. a. Determine the average rate of change of blood alcohol level from x1=2.5tox2=8. Round to 3 decimal places. b. Interpret the results from part (a).7SP 8SP a. Solve the equation 3xx+41=0 and verify the solution graphically on a graphing utility. b. Use the graph to find the solution set to the inequality 3xx+410. c. Use the graph to find the solution set to the inequality 3xx+410.A equation in the variables xandy can be written in the form Ax+By=C, where AandB are not both Zero.An equation of the form x=k where k is a constant represents the graph of a line.An equation of the form y=k where k is a constant represents the graph of a line.Write the formula for the slope of a line between the two distinct points x1,y1andx2,y2.The slope of a horizontal line is and the slope of a vertical line is .A function f is a liner function if fx=, where m represents the slope and 0,b represent the y-intercept.If f is defined on the interval x1,x2, then the average rate of change of f on the interval x1,x2 is given by the formula .The graph of a constant function defined by fx=b is a (horizontal/vertical) line.For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 3x+4y=12 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 2x+y=4 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 2y=5x+2 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 3y=4x+6 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) x=6 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) y=4 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 5y+1=11 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 3x2=4 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 0.02x+0.05y=0.1 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 0.03x+0.07y=0.21 For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 2x=3y For Exercises 9-20, graph the equation and identify the x-andy-intercepts. (See Example 1) 2x=5y Find the average slope of the hill.Find the absolute value of the slope of the storm drainage pipe.The road sign shown in the figure indicate the percent grade of a hill. This gives the slope of the change in elevation per 100 horizontal feet. Given a 2.5 grade, write this as a slope in fractional form.The pitch of a roof is defined as rafterriserafterrun and the fraction is typically written with a denominator of 12. Determine the pitch of the roof from point A to point C .For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 4,7and2,1 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 3,8and4,6 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 17,9and42,6 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 9,4and1,6 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 30,52and22,39 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 100,16and84,30 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 2.6,4.1and9.5,3.7 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 8.5,6.2and5.1,7.9 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 34,6and52,1 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 3,25and4,310 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 36,25and6,5 For Exercises 25-36, determine the slope of the line passing through the given points. (See Example 2) 211,33and11,53 For Exercises 37-42, determine the slope of the line. (See Examples 2-3)For Exercises 37-42, determine the slope of the line. (See Examples 2-3)For Exercises 37-42, determine the slope of the line. (See Examples 2-3)For Exercises 37-42, determine the slope of the line. (See Examples 2-3)For Exercises 37-42, determine the slope of the line. (See Examples 2-3)For Exercises 37-42, determine the slope of the line. (See Examples 2-3)What is the slope of a line perpendicular to the x-axis?What is the slope of a line defined by y=7?If the slope of a line is 45, how much vertical change will be present for a horizontal change of 52 ft?Suppose that y=Pt represents the population of a city at time t. What does Pt represent?What is the slope of a line parallel to the x-axis?What is the slope of a line defined to the x=2?If the slope of a line is 58, how much horizontal change will be present for a vertical change of 216 m?Suppose that y=dt represent the distance that an object travels in time t . What does dt ?For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 2x4y=8 For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 3xy=6 For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 3x=2y4 For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 5x=3y6 For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 3x=4y For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 2x=3y For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 2y6=8 For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 3y+9=6 For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 0.02x+0.06y=0.06 For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) 0.03x+0.04y=0.12 For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) x4+y7=1 For Exercises 51-62, a. Write the equation in slope-intercepts form if possible, and determine the slope and y-intercept. b. Graph the equation using the slope and y-intercept. (See Example 4) x3+y4=1 For Exercises 63-64, determine if the function is linear, constant, or neither. a.fx=34xb.gx=34x3c.hx=34xd.kx=34 For Exercises 63-64, determine if the function is linear, constant, or neither. a.mx=5x+1b.nx=5x+1c.px=5d.qx=5x For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 0,9;m=12 For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 0,4;m=13 For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 1,6;m=3 For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 2,8;m=5 For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 5,3;m=23 For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 4,2;m=32 For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 2,5;m=0 For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 1,3;m=0 For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 3.6,5.1;m=1.2 For Exercises 65-74, a. Use slope-intercepts form to write an equation of the line that passes through the given point and has the given slope. b. Write the equation using function notation where y=fx. (See Example 5) 1.2,2.8;m=2.4 For Exercises 75-78, a. Use slope-intercept form to write an equation of the that passes the two given points. b. Then write the equation using function notation where y=fx. 4,2and0,6 For Exercises 75-78, a. Use slope-intercept form to write an equation of the that passes the two given points. b. Then write the equation using function notation where y=fx. 8,1and0,3 For Exercises 75-78, a. Use slope-intercept form to write an equation of the that passes the two given points. b. Then write the equation using function notation where y=fx. 7,3and4,1 For Exercises 75-78, a. Use slope-intercept form to write an equation of the that passes the two given points. b. Then write the equation using function notation where y=fx. 2,4and1,3 For Exercises 79-80, find slope of the secant line pictured in red. (See Example 6)For Exercises 79-80, find slope of the secant line pictured in red. (See Example 6)The function given by y=fx shows the value of $5000 invested at 5 interest compounded continuously, x years after the money was originally invested. a. Find the average amount earned per year between the 5th year and 10th year. b. Find the average amount earned per year between the 20th year and 25th year. c. Based on the answer from parts (a) and (b), does it appear that the rate at which annual income increases is increasing or decreasing with time?The function given by y=fx shows the average monthly temperature inF for cedar key. The value of x is the month number and x=1 represents January. a. Find the average rate of change in temperature between months 3 and 5 (march and may). b. Find the average rate of change in temperature between month 9 and 11 (September and November). c. Comparing the result in parts (a) and (b), what does a positive rate of change mean in the context of this problem? What does a negative rate of change mean?The number Nt of new cases of a flu outbreak for a given city is given by Nt=500020.04t2, where t is the number of months since the outbreak began. a Find the average rate of change in the number of new flu cases between months 0 and 2, and interpret the result. Round to the nearest whole unit. b. Find the average rate of change in the number of new flu cases between months 4 and 6, and between months 10 and 12. c. Use a graphing utility to graph the function. Use the graph and the average rates of change found in parts (a) and (b) to discuss the pattern of the number of new flu cases.The speed vL (in m/sec) of an ocean wave in deep water is approximated by VL=1.2L, where L (in meters) is the wavelength of the wave. (The wavelength is the distance between two consecutive wave crests.) a. Find the average rate of change in speed between waves that are between 1 m and 4 m in length. b. Find the average rate of change in speed between waves that are between 4 m and 9 m in length. c. Use a graphing utility to graph the function. Using the graph and the results from parts (a) and (b), what does the difference in the rates of change mean?For Exercises 85-90, determine the average rate of change of the function on the given interval. (See Example 7) fx=x23a.on0,1b.on1,3c.on2,0 For Exercises 85-90, determine the average rate of change of the function on the given interval. (See Example 7) gx=2x2+2a.on0,1b.on1,3c.on2,0 For Exercises 85-90, determine the average rate of change of the function on the given interval. (See Example 7) hx=x3a.on1,0b.on0,1c.on1,2 For Exercises 85-90, determine the average rate of change of the function on the given interval. (See Example 7) kx=x32a.on1,0b.on0,1c.on1,2 For Exercises 85-90, determine the average rate of change of the function on the given interval. (See Example 7) mx=xa.0,1b.1,4c.4,9 For Exercises 85-90, determine the average rate of change of the function on the given interval. (See Example 7) nx=x1a.1,2b.2,5c.5,10 For Exercises 91-98, use the graph to solve the equation and inequalities. Write the solution to the inequalities in interval notation. (See Examples 8-9) a.2x+4=x+1b.2x+4x+1c.2x+4x+1 For Exercises 91-98, use the graph to solve the equation and inequalities. Write the solution to the inequalities in interval notation. (See Examples 8-9) a.4x2=3x+5b.4x23x+5c.4x23x+5 For Exercises 91-98, use the graph to solve the equation and inequalities. Write the solution to the inequalities in interval notation. (See Examples 8-9) a.3x+1=x3b.3x+1x3c.3x+1x3 For Exercises 91-98, use the graph to solve the equation and inequalities. Write the solution to the inequalities in interval notation. (See Examples 8-9) a.x2=2x5b.x22x5c.x22x5 For Exercises 91-98, use the graph to solve the equation and inequalities. Write the solution to the inequalities in interval notation. (See Examples 8-9) a.3x+2+1=x+5b.3x+2+1x+5c.3x+2+1x+5 For Exercises 91-98, use the graph to solve the equation and inequalities. Write the solution to the inequalities in interval notation. (See Examples 8-9) a.4x5+3x=3x+1b.4x5+3x3x+1c.4x5+3x3x+1 For Exercises 91-98, use the graph to solve the equation and inequalities. Write the solution to the inequalities in interval notation. (See Examples 8-9) a.42x+1+12+x=0b.42x+1+12+x0c.42x+1+12+x0 For Exercises 91-98, use the graph to solve the equation and inequalities. Write the solution to the inequalities in interval notation. (See Examples 8-9) a.841x72x=0b.841x72x0c.841x72x0 Explain how you can determine from a linear equation Ax+By=C (AandB not both zero) whether the line is slanted, horizontal, or vertical.Explain how you can determine from a linear equation Ax+By=C (AandB not both zero) whether the line passes through the origin.What is the benefit of writing an equation of a line in slope-intercept form?Explain how the average rate of change of a function f on the interval x1,x2 is related to slope.Determine the area in the second quadrant enclosed by the equation y=2x+4andthex-andy-axes.Determine the area enclosed by the equations. y=x+6y=2x+6y=0 Determine the area enclosed by the equations. y=12x2y=13x2y=0 Determine the area enclosed by the equations. y=4x22y=0 Consider the standard form of a linear equation Ax+By=C in the case where B0. a. Write the equation in slope-intercept form. b. Identify the slope in terms of the coefficients AandB . c. Identify the y-intercept in terms of the coefficients BandC.Use the results from Exercise 107 to determine the slope and y-intercept for the graphs of the lines. a.5x9y=6b.0.052x0.013y=0.39 For Exercises 109-112, solve the equation in part (a) and verify the solution on a graphing calculator. Then use the graph to find the solution set to the inequalities in parts (b) and (c). Write the solution sets to the inequalities in interval notation. (See Example 9) a.3.12.2t+1=6.3+1.4tb.3.12.2t+16.3+1.4tc.3.12.2t+16.3+1.4t For Exercises 109-112, solve the equation in part (a) and verify the solution on a graphing calculator. Then use the graph to find the solution set to the inequalities in parts (b) and (c). Write the solution sets to the inequalities in interval notation. (See Example 9) a.11.24.6c3+1.8c=0.4c+2b.11.24.6c3+1.8c0.4c+2c.11.24.6c3+1.8c0.4c+2 For Exercises 109-112, solve the equation in part (a) and verify the solution on a graphing calculator. Then use the graph to find the solution set to the inequalities in parts (b) and (c). Write the solution sets to the inequalities in interval notation. (See Example 9) a.2x3.84.6=7.2b.2x3.84.67.2c.2x3.84.67.2 For Exercises 109-112, solve the equation in part (a) and verify the solution on a graphing calculator. Then use the graph to find the solution set to the inequalities in parts (b) and (c). Write the solution sets to the inequalities in interval notation. (See Example 9) a.x1.7+4.95=11.15b.x1.7+4.9511.15c.x1.7+4.9511.15 For Exercises 113-114, graph the lines in (a)-(c) on the standard viewing window. Compare the graphs. Are they exactly the same? If not, how are they different? a.y=3x+1b.y=2.99x+1c.y=3.01x+1 For Exercises 113-114, graph the lines in (a)-(c) on the standard viewing window. Compare the graphs. Are they exactly the same? If not, how are they different? a.y=x+3b.y=x+2.99c.y=x+3.01 Use the point-slope formula to find an equation of the line passing through the point 5,2 and having slope 3. Write the answer in slope-intercepts form.Write an equation of the line passing through the points 2,5and7,3.3SP Write an equation of the line passing through the point 8,4 and perpendicular to the line defined by y=16x+3.5SP Repeat Example 6 in the case where the vendor can cut the cost to $0.40 per cup of lemonade, and sell lemonades for $1.50 per cup.Suppose that y represents the average consumer spending on television services per year (in dollars), and that x represents the number of year since 2004. a. Use the data points (2,308) and (6,408) to write a linear equation relating y to x . b. Interpret the meaning of the slope in the context of this problem. c. Interpret the meaning of the y-intercept in the context of this problem. d. Use the model from part (a) to estimate the average consumer spending on television services for the year 2007.The data given represent the class averages for individual students based on the number of absences from class. a. Find the equation of the least-squares regression line. b. Use the model from part (a) to approximate the average for a student who misses 6 classes.Given a point x1,y1 on a line with slope m , the point-slope formula is given by .If two nonvertical lines have the same slope but different y-intercepts, then the lines are (parallel/perpendicular).If m1andm2 represent the slope of two nonvertical perpendicular lines, then m1m2=.Suppose that y=Cx represents the cost to produce x items, and that y=Rx represents the revenue for selling x items. The profit Px of producing and selling x items is defined by Px=.For Exercises 5-20, use the point-slope formula to write an equation of the line having the given conditions. Write the answer in slope-intercepts form (if possible). (See Example 1-2) Passesthrough3,5andm=2.For Exercises 5-20, use the point-slope formula to write an equation of the line having the given conditions. Write the answer in slope-intercepts form (if possible). (See Example 1-2) Passesthrough4,6andm=3.7PE 8PE For Exercises 5-20, use the point-slope formula to write an equation of the line having the given conditions. Write the answer in slope-intercepts form (if possible). (See Example 1-2) Passesthrough3.4,2.6andm=1.2.For Exercises 5-20, use the point-slope formula to write an equation of the line having the given conditions. Write the answer in slope-intercepts form (if possible). (See Example 1-2) Passesthrough2.2,4.1andm=2.4.11PE 12PE 13PE For Exercises 5-20, use the point-slope formula to write an equation of the line having the given conditions. Write the answer in slope-intercepts form (if possible). (See Example 1-2) Passesthrough0,6and11,0.For Exercises 5-20, use the point-slope formula to write an equation of the line having the given conditions. Write the answer in slope-intercepts form (if possible). (See Example 1-2) Passesthrough2.3,5.1and1.9,3.7.For Exercises 5-20, use the point-slope formula to write an equation of the line having the given conditions. Write the answer in slope-intercepts form (if possible). (See Example 1-2) Passesthrough1.6,4.8and0.8,6.17PE For Exercises 5-20, use the point-slope formula to write an equation of the line having the given conditions. Write the answer in slope-intercepts form (if possible). (See Example 1-2) Passesthrough5,1andm=0.19PE For Exercises 5-20, use the point-slope formula to write an equation of the line having the given conditions. Write the answer in slope-intercepts form (if possible). (See Example 1-2) Passesthrough47,310andtheslopeisundefined.21PE 22PE For Exercises 23-28, the slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible. m=311 24PE 25PE For Exercises 23-28, the slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible. m=10 27PE 28PE For Exercises 29-36, determine if the lines defined by the given equation are parallel, perpendicular, or neither. y=2x3y=12x+7 30PE For Exercises 29-36, determine if the lines defined by the given equation are parallel, perpendicular, or neither. 8x5y=32x=54y+1 32PE 33PE For Exercises 29-36, determine if the lines defined by the given equation are parallel, perpendicular, or neither. 3y=5x=1 35PE 36PE For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form Ax+By=C with fractional coefficients. (See Example 3-4) Passesthrough2,5andisparalleltothelinedefinedby2x+y=6.For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form Ax+By=C with fractional coefficients. (See Example 3-4) Passesthrough3,1andisparalleltothelinedefinedby3x+y=4.For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form Ax+By=C with fractional coefficients. (See Example 3-4) Passesthrough6,4andisperpendiculartothelinedefinedbyx5y=1.For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form Ax+By=C with fractional coefficients. (See Example 3-4) Passesthrough5,4andisperpendiculartothelinedefinedbyx2y=7.For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form Ax+By=C with fractional coefficients. (See Example 3-4) Passesthrough6,8andisparalleltothelinedefinedby3x=7y+5.For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form Ax+By=C with fractional coefficients. (See Example 3-4) Passesthrough7,6andisparalleltothelinedefinedby2x=5y4.43PE For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form Ax+By=C with fractional coefficients. (See Example 3-4) Passesthrough3.6,1.2andisperpendiculartothelinedefinedby4x=9y.For Exercises 45-50, write an equation of the line that satisfies the given conditions. Passesthrough8,6andisparalleltothex-axis.46PE 47PE 48PE For Exercises 45-50, write an equation of the line that satisfies the given conditions. Passesthrough61.5,47.6andisparalleltothelinedefinedbyx=12.For Exercises 45-50, write an equation of the line that satisfies the given conditions. Passesthrough0.004,0.009andisparalleltothelinedefinedbyy=6.A sales person makes a base salary of $400 per week plus 12 commission on sales. (See Example 5) a. Write a linear function to model the sales person's weekly salary Sx for x dollars in sales. b. Evaluate S8000 and interpret the meaning in the context of this problem.At a parking garage in a large city, the charge for parking consists of a flat fee of $2.00 plus $1.50/hr. a. Write a linear function to model the cost for parking Pt fort t hours. b. Evaluate P1.6 and interpret the meaning in the context of this problem.Millage rate is the amount per $1000 that is often used to calculate property tax. For example, a home with a 60,000 taxable value in a municipality with a 19 mil tax rate would require 0.019$60,000=$1140 in property taxes. In one county, homeowners pay a flat tax of $172 plus a rate of 19 mil on the taxable value of a home. a. Write a linear function that represents the total property tax Tx for a home with a taxable value of x dollars. b. Evaluate T80,000 and interpret the meaning in the context of this problem.The average water level in a retention pond is 6.8 ft. During a time of drought, the water level decreases at a rate of 3 in./day. a. Write a linear function W that represents the water level Wtinftt days after a drought begins. b. Evaluate W20 and interpret the meaning in the context of this problem.For Exercises 55-56, the fixed and variable costs to produce an item are given along with the price at which an item is sold. (See Example 6) a. Write a linear cost function that represents the cost Cx to produce x items. b. Write a linear revenue function that represents the revenue Rx for selling x items. c. Write a linear profit function that represents the profit Px for producing and selling x items. d. Determine the break-even point. Fixedcost:$2275Variablecostperitem:$34.50Priceatwhichtheitemissold:$80.00 For Exercises 55-56, the fixed and variable costs to produce an item are given along with the price at which an item is sold. (See Example 6) a. Write a linear cost function that represents the cost Cx to produce x items. b. Write a linear revenue function that represents the revenue Rx for selling x items. c. Write a linear profit function that represents the profit Px for producing and selling x items. d. Determine the break-even point. Fixedcost:$5625Variablecostperitem:$0.40Priceatwhichtheitemissold:$1.30 57PE 58PE A small business makes cookies and sells them at the farmerâ€™s market. The fixed monthly cost for use of a Health Department-approved kitchen and rental space at the farmer's market is $790. The cost of labor, taxes, and ingredients for the cookies amounts to $0.24 per cookie, and the cookies sell for $6.00 per dozen. (See Example 6) a. Write a linear cost function representing the cost Cx to produce x dozen cookies per month. b. Write a linear revenue function representing the revenue Rx for selling x dozen cookies. c. Write a linear profit function representing the profit for producing and selling x dozen cookies in a month. d. Determine the number of cookies (in dozens) that must be produced and sold for a monthly profit. e. If 150 dozen cookies are sold in a given month, how much money will the business make or lose?A lawn service company charges $60 for each lawn maintenance call. The fixed monthly cost of $680 includes telephone service and depreciation of equipment. The variable costs include labor, gasoline, and taxes and amount to $36 per lawn. a. Write a linear cost function representing the monthly cost Cx for x maintenance calls. b. Write a linear revenue function representing the monthly revenue Rx for x maintenance calls. c. Write a linear profit function representing the monthly profit Px for x maintenance calls. d. Determine the number of lawn maintenance calls needed per month for the company to make money. e. If 42 maintenance calls are made for a given month, how much money will the lawn service make or lose?The data in the graph show the wind speed y (in mph) for Hurricane Katrina versus the barometric pressure x (in millibars, mb). (See. Example 7) a. Use the points (950, 110) and (1000, 50) to write a linear for these data. b. Interpret the meaning of the slope in the context of this problem. c. Use the model from part (a) to estimate the wind speed for a hurricane with a pressure of 900 mb. d. The lowest barometric pressure ever recorded for an Atlantic hurricane was 882 mb for Hurricane Wilma in 2005. Would it be reasonable to use the model from part (a) to estimate the wind speed for a hurricane with a pressure of 800 mb?Caroline adopted a puppy named Dodger from an animal shelter in Chicago. She recorded Dodgerâ€™s weight during the first two months. The data in the graph show Dodgerâ€™s weight y (in lb), x dates after adoption. a. Use the points (0, 11) and (40, 22) to write a linear for these data. b. Interpret the meaning of the slope in context. c. Interpret the meaning of the y-intercept in context. d. If this linear trend continues during Dodgerâ€™s growth period, how long will it take Dodger to reach 90 of his expected full-grown weight of 70 lb? Round to the nearest day. e. Is the model from part (a) reasonable long term?A paediatrician records the age xinyr and average height yininches for girls between the ages of 2 and 10. a. Use the points (2, 35) and (6, 46) to write a linear model for these data. b. Interpret the meaning of the slope in context. c. Use the model to forecast the average height of 11-yr-old girls. d. If the height of a girl at age 11 is 90 of her full-grown adult height, use the result of part (c) to estimate the average height of adult women. Round to the nearest tenth of an inch.The graph shows the number of students enrolled in public colleges for selected years. The x variable represents the number of years since 1990 and the y variable represents the number of students (in millions). a. Use the points (4, 11.2) and (14, 13.0) to write a linear model for these data. b. Interpret the meaning of the slope in the context of this problem. c. Interpret the meaning of the y-intercept in the context of this problem. d. In the event that the linear trend continues beyond the last observed data point, use the model in part (a) to predict the number of students enrolled in public colleges for the year 2020.The table gives the number of calories and the amount of cholesterol for selected fast food hamburgers. a. Graph the data in a scatter plot using the number of calories as the independent variable x and the amount of cholesterol as the dependent variable y . b. Use the data points (480, 60) and (720, 90) to write a linear function that defines the amount of cholesterol cx as a linear function of the number of calories x . c. Interpret the meaning of the slope in the context of this problem. d. Use the model from part (b) to predict the amount of cholesterol for a hamburger with 650 calories.The table gives the average gestation period for selected animals and their corresponding average longevity. a. Graph the data in a scatter plot using the number of days for gestation as the independent variable x and the longevity as the dependent variable y . b. Use the data points (44, 8.5) and (620, 35) to write a linear function that defines longevity Lx as a linear function of the length of the gestation period x . Round the slope to 3 decimal places and the y-intercept to 2 decimal places. c. Interpret the meaning of the slope in the context of this problem. d. Use the model from part (b) to predict the longevity for an animal with an 80-day gestation period. Round to the nearest year.67PE 68PE 69PE 70PE The graph in Exercise 61 shows the wind speed y (in mph) of a hurricane versus the barometric pressure x (in mb). The table gives a partial list of data from the graph. (See Example 8) a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the y-intercept to the nearest whole unit. b. Use a graphing utility to graph the regression line and the observed data. c. Use the model in part (a) to approximate the wind speed of a hurricane with a barometric pressure of 900 mb. d. By how much do the results of part (c) differ from the result of Exercise 61(c)?72PE The graph in Exercise 63 shows the average height of girls based on their age. The data in the table give the average height y (in inches) for girls of age x (in yr). a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the y-intercept to 1 decimal place. b. Use a graphing utility to graph the regression line and the observed data. c. Use the model in part (a) to approximate the average height of 11-yr-old girls. d. If the height of a girl at age 11 is 90 of her full-grown adult height, use the result of part (c) to estimate the average height of adult women. Round to the nearest tenth of an inch. e. By how much do the results of part (d) differ from the result of Exercise 63(d)?The graph in Exercise 64 shows the number of student y enrolled in public colleges for selected years x, where x is the number of years since 1990. The table gives a partial list of data from the graph. a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the y-intercept to 1 decimal place. b. Use a graphing utility to graph the regression line and the observed data. c. Assuming that the linear trend continues use the model from part (a) to predict the number of students enrolled in public colleges for the year 2020. d. By how much do the results of part (c) differ from the result of Exercise 64(d)?75PE 76PE 77PE 78PE 79PE 80PE 81PE 82PE 83PE 84PE 85PE 86PE 87PE 88PE 89PE 90PE 91PE 92PE 1PRE 2PRE 3PRE 4PRE 5PRE 6PRE 7PRE 8PRE 9PRE 10PRE

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