In Exercises 1 to 10, find the slope of the line that passes through the given points. 1. (3,4) and (1,7) 3. (4,0) and (0,2) 5. (3-7) and (3,2) 7. (-3,4) and (-4,-2) 9. *2 (-2,4) and (5.1) 4 (-3,4) and (2,4) 6. (0,0) and (3,0) & (-5-1) and (-3,4) 10.
In Exercises 1 to 10, find the slope of the line that passes through the given points. 1. (3,4) and (1,7) 3. (4,0) and (0,2) 5. (3-7) and (3,2) 7. (-3,4) and (-4,-2) 9. *2 (-2,4) and (5.1) 4 (-3,4) and (2,4) 6. (0,0) and (3,0) & (-5-1) and (-3,4) 10.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:EXERCISE SET 2.3
In Exercises 1 to 10, find the slope of the line that passes
through the given points.
1. (3,4) and (1,7)
3. (4,0) and (0, 2)
5. (3-7) and (3,2)
7. (-3,4) and (-4,-2)
9. (-4) (¹)
2 (-2,4) and (5,1)
4. (-3,4) and (2,4)
6. (0,0) and (3,0)
8 (-5,-1) and (-3,4)
In Exercises 11 to 14, find the slope of the line that
passes through the given points.
11. (3/3)) and (3+Af(3 + A))
12. (-2,-2)) and (-2+(-2+A)
13, (0,/(0)) and (h.)
14. (a,f(a)) and (a + k,f(a+h))
31. 2x-5--15
33. x+2y=6
10.
196 CHAPTER 2 FUNCTIONS AND GRAPHS
32. 3x - 4y - 8
34. x-3y=9
40. y-intercept (0, -1), slope
41. Through (-3,2), slope-4
42. Through (-5,-1), slope-3
43. Through (3, 1) and (-1.4)
44. Through (5.-6) and (2.-8)
45. Through (7,11) and (2,-1)
46. Through (-5,6) and (-3,-4)
In Exercises 35 to 46, find the equation of the indicated
line. Write the equation in the form y= mx + b.
35. -intercept (0, 3), slope 11
36. y-intercept (0,5), slope-21
37. y-intercepe (0.). slope
38. y-intercept (a). stope-
39. y-intercept (0,4), slope 0
In Exercises 47 to 58, find the equation of the line, in
slope-intercept form, that satisifies the given conditions.
47. The graph is parallel to the graph of y2x + 3 and passes
through the point whose coordinates are (2,-4).
48. The graph is parallel to the graph of y=-x+1 and passes
through the point whose coordinates are (-2,4).
49. The graph is parallel to the graph of y-+3 and passes
through the point whose coordinates are (-4,2)
50. The graph is parallel to the graph of y-x-1 and passes
through the point whose coordinates are (-3,-5)
51. The graph is parallel to the graph of 2x-5y-2 and passes
through the point whose coordinates are (5, 2)
52. The graph is parallel to the graph of x + 3y 4 and passes
through the point whose coordinates are (-3,-1).
In Exercises 15 to 26, graph y as a function of x by
finding the slope and y-intercept of each line.
15. y-21-4
16. y=-x+1
17. y=x+1
19. y=-2x+3
21. y 3
23. y = 2x
25. yax
18. y=-x+4
In Exercises 27 to 34, graph each equation by first
writing the equation in slope-intercept form. Check the
graph by finding the x- and y-intercepts.
27. 2x+y = 5
28. x-y=4
29. 4x+3y-12-0
30, 2x+3y+6=0
20. y 3-1
53. The graph is perpendicular to the graph of y=2x-5 and passes
through the point whose coordinates are (3,-4).
22. y = -2
24
54. The graph is perpendicular to the graph of y=-x+ 3 and
passes through the point whose coordinates are (-5,2).
3
55. The graph is perpendicular to the graph of y=-x+ 1 and
passes through the point whose coordinates are (-6,0).
y=-3x
26. y-x
ya
56. The graph is perpendicular to the graph of 3x-2y5 and
passes through the point whose coordinates are (-3,4).
57. The graph is perpendicular to the graph of -x-4-6 and
passes through the point whose coordinates are (5,2)
58. The graph is perpendicular to the graph of 5x-y-2 and
passes through the point whose coordinates are (10,-2).
59. Find the value of a in the domain of f(x)=2x+3 for which
fa) -1.
60. Find the value of a in the domain of fox)-4-3x for which
fla) 7.
1500
61. Find the value of a in the domain of fix)-1-4x for which
fla) 3.
21500
62. Find the value of a in the domain of f(x)+2 for which
fa)-4.
1400
In Exercises 63 to 66, find the zero of f. Verify that the
solution of f(x)=0 is the same as the x-coordinate of
the x-intercept of the graph of y = f(x).
63. /0x)-3x-12
64. f(x)=-2x-4
1480
67. Oceanography The graph below shows the relationship
between the speed of sound in water and the temperature of the
water. Find the slope of this line, and write a sentence that
explains the meaning of the slope in the context of this problem.
(2012)
(28 150
20 22 24 26 28 30
Temperature in degrees C)
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