ercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. The point (-1, 3) lies in quadrant 2. The point (4, in the rectangular coordinate system. 3x-6. ) lies on the graph of the equation y 3. Any point that lies on the x-axis has y-coordinate equal to 4. The y-intercept of the graph of y -2x + 6 is 5. The x-intercept of the graph of 2x + 5y 10 is 6. The distance from the origin to the point (-3, 4) is CONCEPT PREVIEW Determine whether each statement is true or false. If false, explain why. 7. The graph of y = x² + 2 has no x-intercepts. 8. The graph of y = x² – 2 has two x-intercepts. 9. The midpoint of the segment joining (0, 0) and (4, 4) is 2. 10. The distance between the points (0, 0) and (4, 4) is 4. Give three ordered pairs from each table. See Example 1. 11. x 12. У У х dgeng -5 3 -1 -21 8. 18 -9 borobno 5 6. 6. -17 9- -21 14. Number of U.S. Viewers of the Super Bowl 13. Percent of High School Students Who Smoke Viewers (millions) Year Percent Year 86.8 2002 35 1999 89.8 2004 29 (b) 2001 90.7 2006 22 2003 97.4 2008 23 2005 106.5 2010 20 2007 111.4 2012 20 2009 111.5 m ow 2014 isvlo Source: Centers for Source: www.tvbythenumbers.com Disease Control and Prevention. For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid- naint Maf line segment PQ. See Examples 2 and 5(a). 3584t 3. Year Income (in dollars) 13,359 1990 17,604 2000 22,315 2010 23,021 2011 2013 23,834 Source: U.S. Census Bureau. 44. Public College Enrollment Enrollments in public colleges for recent years are shown in the table. Assuming a linear relationship, estimate the enrollments for (a) 2003 and (b) 2009. Give answers to the nearest tenth of thousands if applicable. Enrollment (in thousands) Year 2000 11,753 2006 13,180 2012 14,880 Source: National Center for Education Statistics. 45. Show that if M is the midpoint of the line segment with endpoints P(x1, y1) and Q(x2, y2), then d(P, M) = d(M, Q). d(P, M) + d(M, Q) = d(P, Q) and %3D 46. Write the distance formula d = V(x2 – x )² + (y2 – yı)² using a rational exponent. %3D For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. 1 = --x + 2 2 47. 48. y 49. 2x + 3y = 5 r-2· 50. 3x - 2y = 6 52.) y = x² + 2 51. y = x2 54. y = Vx – 3 55. y= |x – 2| 53. y = Vx – 3 dw5 of 57. y= x³ aoil 56. y = -|x+ 4|| 58. y= -x³ Concept Check Answer the following. 59. If a vertical line is drawn through the point (4, 3), at what point will it intersect the x-axis? 60. If a horizontal line is drawn through the point (4, 3), at what point will it intersec the y-axis? 61. If the point (a, b) is in the second quadrant, then in what quadrant is (a, -b (-a,b)? (-a, -b)? (b, a)? 62. Show that the points (-2, 2), (13, 10), (21, –5), and (6, –13) are the vertices a rhombus (all sides equal in length).