44 CHAPTER 1 Graphs 10. Multiple Choice Choose the formula for finding the slope m of a nonvertical line that contains the two distinct points ( ) x y , 1 1 and ( ) x y , . 2 2 (a) = − − ≠ m y x y x x y 2 2 1 1 1 1 (b) = − − ≠ m y x x y y x 2 1 2 1 1 2 (c) = − − ≠ m x x y y y y 2 1 2 1 1 2 (d) = − − ≠ m y y x x x x 2 1 2 1 1 2 11. Multiple Choice Choose the correct statement about the graph of the line = − y 3. (a) The graph is vertical with x-intercept −3. (b) The graph is horizontal with y-intercept −3. (c) The graph is vertical with y-intercept −3. (d) The graph is horizontal with x-intercept −3. 12. Multiple Choice Choose the point-slope equation of a nonvertical line with slope m that passes through the point ( ) x y , . 1 1 (a) + = + y y mx x 1 1 (b) − = − y y mx x 1 1 (c) ( ) + = + y y m x x 1 1 (d) ( ) − = − y y m x x 1 1 2. The slope of a vertical line is ; the slope of a horizontal line is . 3. For the line + = x y 2 3 6, the x-intercept is and the y-intercept is . 4. True or False The equation + = x y 3 4 6 is written in general form. 5. True or False The slope of the line = + y x 2 3 5 is 3. 6. True or False The point ( ) 1, 2 is on the line + = x y 2 4. 7. Two nonvertical lines have slopes m1 and m ,2 respectively. The lines are parallel if and the are unequal; the lines are perpendicular if . 8. The lines = + y x2 3 and = + y ax 5 are parallel if = a . 9. The lines = − y x2 1 and = + y ax 2 are perpendicular if = a . Skill Building In Problems 13–16, (a) find the slope of the line and (b) interpret the slope. 13. x y –2 2 (0, 0) (2, 1) 2 –1 14. x y –2 2 (–2, 1) (0, 0) 2 –1 15. x y –2 2 (–2, 2) (1, 1) 2 –1 16. x y –2 2 (–1, 1) (2, 2) 2 –1 In Problems 17–24, plot each pair of points and determine the slope of the line containing the points. Graph the line. 17. ( ) ( ) 2, 3 ; 4, 0 18. ( ) ( ) 4, 2 ; 3, 4 19. 2, 3 ; 2, 1 ( ) ( ) − 20. 1, 1 ; 2, 3 ( ) ( ) − 21. ( ) ( ) − − − 3, 1;2, 1 22. ( ) ( ) − 4, 2 ; 5, 2 23. 1,2; 1, 2 ( ) ( ) − − − 24. ( ) ( ) 2, 0 ; 2, 2 In Problems 25–32, graph the line that contains the point P and has slope m. 25. ( ) = = P m 1, 2 ; 3 26. ( ) = = P m 2, 1 ; 4 27. ( ) = = − P m 2, 4 ; 3 4 28. ( ) = = − P m 1, 3 ; 2 5 29. ( ) = − = P m 1, 3 ; 0 30. ( ) = − = P m 2, 4; 0 31. ( ) = P 0, 3 ; slope undefined 32. ( ) = − P 2, 0 ; slope undefined In Problems 33–38, a point on a line and its slope are given. Find the point-slope form of the equation of the line. 33. ( ) = = P m 1, 2 ; 3 34. ( ) = = P m 2, 1 ; 4 35. ( ) = = − P m 2, 4 ; 3 4 36. P m 1, 3 ; 2 5 ( ) = = − 37. ( ) = − = P m 1, 3 ; 0 38. ( ) = − = P m 2, 4 ; 0 In Problems 39–44, the slope and a point on a line are given. Use this information to locate three additional points on the line.Answers may vary. [Hint: It is not necessary to find the equation of the line. See Example 2.] 39. Slope 4; point ( ) 1, 2 40. Slope 2; point ( ) −2, 3 41. Slope − 3 2 ; point ( ) − 2, 4 42. Slope 4 3 ; point ( ) −3, 2 43. Slope −2; point ( ) − − 2, 3 44. Slope −1; point ( ) 4, 1 In Problems 45–52, find an equation of the line L. 45. x y –2 2 (0, 0) (2, 1) 2 –1 L 46. x y –2 2 (–2, 1) (0, 0) 2 –1 L 47. x y –2 2 (–1, 3) (1, 1) 3 –1 L 48. x y –2 2 (–1, 1) (2, 2) 2 –1 L
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