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10. 2x – 5 > x; x > 5 24. x = 6; y = 6 11. 9x – 3 > 6x + 5; x > 8/3 31. C

10. 2x – 5 > x; x > 5 24. x = 6; y = 6 11. 9x – 3 > 6x + 5; x > 8/3 31. C 12. X = 45; y = 60 32. F 13. X = 6; y = 15 33. B 14. X = 25; y = 40 34. C 15. X = 60; y = 60 40. 152 ° 16. Yes 41. 25 ° 17. No 42. 155 °

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10. 2x – 5 > x; x > 5 24. x = 6; y = 6 11. 9x – 3 > 6x + 5; x > 8/3 31. C

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  1. 10. 2x – 5 > x; x > 5 24. x = 6; y = 6 11. 9x – 3 > 6x + 5; x > 8/3 31. C 12. X = 45; y = 60 32. F 13. X = 6; y = 15 33. B 14. X = 25; y = 40 34. C 15. X = 60; y = 60 40. 152° 16. Yes 41. 25° 17. No 42. 155° 18. No 43. Conv. Alt Ext Angles 19. No 44. Conv. Alt Int Angles 20. Yes 45. Conv. Same-Side Int Angles 21. yes

  2. Warm Up Find the value of m. 1. 2. 3. 4. undefined 0

  3. The slopeof a line in a coordinate plane is a number that describes the steepness of the line. Any two points on a line can be used to determine the slope.

  4. Remember! A fraction with zero in the denominator is undefined because it is impossible to divide by zero. AB AC AD CD Example 1: Use the slope formula to determine the slope of each line. The slope is undefined.

  5. One interpretation of slope is a rate of change. If y represents miles traveled and x represents time in hours, the slope gives the rate of change in miles per hour.

  6. Example 2: Justin is driving from home to his college dormitory. At 4:00 p.m., he is 260 miles from home. At 7:00 p.m., he is 455 miles from home. Graph the line that represents Justin’s distance from home at a given time. Find and interpret the slope of the line. Use the points (4, 260) and (7, 455) to graph the line and find the slope. The slope is 65, which means Justin is traveling at an average of 65 miles per hour.

  7. Another way to look at perpendicular slopes is OPPOSITE RECIPROCALS, meaning 2/3 and -3/2.

  8. WX and YZ for W(3, 1), X(3, –2), Y(–2, 3), and Z(4, 3) Example 3a Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. Vertical and horizontal lines are perpendicular.

  9. KL and MN for K(–4, 4), L(–2, –3), M(3, 1), and N(–5, –1) Example 3b Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. The slopes are not the same, so the lines are not parallel. The product of the slopes is not –1, so the lines are not perpendicular.

  10. BC and DE for B(1, 1), C(3, 5), D(–2, –6), and E(3, 4) Example 3c Graph each pair of lines. Use slopes to determine whether the lines are parallel, perpendicular, or neither. The lines have the same slope, so they are parallel.

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