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8 Exercises KEYWORD: MA7 5-8 (2-5)B Writing Linear Equations - Parallel & Perp. GUIDED PRACTICE 1. Vocabulary AMPLE 1 p. 349 ? Ss se s ’ T H a G WRI Cl Name _______________________________ (2-5)B KEYWORD: MA7 Parent lines have the same slope. (Parallel or Perpendicular) Identify which lines are parallel. 2. y = 6; y = 6x + 5; y = 6x - 7; y = -8 3 x - 1; y = -2x; y - 3 = _ 3 (x - 5); y - 4 = -2 (x + 2) 3. y = _ 4 4 AMPLE 2 p. 350 AMPLE 3 p. 351 4. Geometry Show that ABCD is a trapezoid. (Hint: In a trapezoid, exactly one pair of opposite sides is parallel.) Identify which lines are perpendicular. 3 x + 2; y = -1; x = 3 2 x - 4; y = - _ 5. y = _ 3 2 p. 351 AMPLE 5 p. 352 7. Geometry Show that PQRS is a rectangle. (Hint: In a rectangle, all four angles are right angles.) 8. Write an equation in slope-intercept form for the line that passes through (5, 0) and is perpendicular to the line described by y = - __52 x + 6. {]Êx® { È]ÊÓ® Ó Ý { ä Ó { È Ó]Ê£® Ó 3 x - 4; y - 4 = -7 (x + 2); 6. y = - _ 7 7 (x - 3) 1 (x - 4); y - 7 = _ y-1=_ 7 3 AMPLE 4 Þ Ó]Êx® È Þ È +Ó]ÊÈ® ,n]Êή { Ó *£]Ê{® -Ç]Ê£® ä Ó { È Ý n PRACTICE AND PROBLEM SOLVING nt Practice See Example 1 2 3 4 5 ractice p. S13 actice p. S32 Identify which lines are parallel. 5 x - 4; x = -9 5 x + 8; y = - _ 9. x = 7; y = - _ 6 6 1 (x - 14); y + 1 = _ 1x 10. y = -x; y - 3 = -1 (x + 9); y - 6 = _ 2 2 1 x - 1; -x + 2y = 17; 3x + y = 27 11. y = -3x + 2; y = _ 2 12. Geometry Show that LMNP is a parallelogram. Identify which lines are perpendicular. 1 x; y = -6x 1 x; y = - _ 13. y = 6x; y = _ 6 6 { 1 x + 5; y = 0; x = 6 14. y - 9 = 3 (x + 1); y = - _ 3 15. x - 6y = 15; y = 3x - 2; y = -3x - 3; y = -6x - 8; 3y = -x - 11 Worksheet adapted from 2007 Holt, Rinehart and Winston Algebra 1 Book ä]Ê{® Ó ÊÎ]Êä® { Þ Î]Êä® Ó ä Ó Ó { *ä]Ê{® { (2-5)B Writing Linear Equations - Parallel & Perp. (2-5)B 16. Geometry Show that ABC is a right triangle. 17. Write an equation in slope-intercept form for the line that passes through (0, 0) and is parallel to the line described by y = - __67 x + 1. Þ Ý n Ç]ÊÓ® 1x+2 20. y = 2x - 1 and y = _ 2 { Ó Î]Êή { Without graphing, tell whether each pair of lines is parallel, perpendicular, or neither. 18. x = 2 and y = -5 È ä È {]ÊÇ® n 19. y = 7x and y - 28 = 7(x - 4) 1 (x - 3) and y + 13 = _ 1 (x + 1 ) 21. y - 3 = _ 4 4 Write an equation in slope-intercept form for the line that is parallel to the given line and that passes through the given point. 1 x + 5; 4, -3 22. y = 3x - 7; (0, 4) 23. y = _ 24. 4y = x; (4, 0) ) ( 2 25. y = 2x + 3; (1, 7) 26. 5x - 2y = 10; (3, -5) 27. y = 3x - 4; (-2, 7) 28. y = 7; (2, 4) 29. x + y = 1; (2, 3) 30. 2x + 3y = 7; (4, 5) 31. y = 4x + 2; (5, -3) 1 x - 1; 0, -4 32. y = _ ) ( 2 33. 3x + 4y = 8; (4, -3) Write an equation in slope-intercept form for the line that is perpendicular to the given line and that passes through the given point. 34. y = -3x + 4; (6, -2) 35. y = x - 6; (-1, 2) 36. 3x - 4y = 8; (-6, 5) 37. 5x + 2y = 10; (3, -5) 38. y = 5 - 3x; (2, -4) 39. -10x + 2y = 8; (4, -3) 40. 2x + 3y = 7; (4, 5) 41. 4x - 2y = -6; (3, -2) 42. -2x - 8y = 16; (4, 5) 43. y = -2x + 4; (-2, 5) 44. y = x - 5; (0, 5) 45. x + y = 2; (8, 5) 46. Write an equation describing the line that is parallel to the y-axis and that is 6 units to the right of the y-axis. 47. Write an equation describing the line that is perpendicular to the y-axis and that is 4 units below the x-axis. 48. Critical Thinking Is it possible for two linear functions whose graphs are parallel lines to have the same y-intercept? Explain. 49. Estimation Estimate the slope of a line that is perpendicular to the line through (2.07, 8.95) and (-1.9, 25.07). 50. Write About It Explain in words how to write an equation in slope-intercept form that describes a line parallel to y - 3 = -6(x - 3). Worksheet adapted from 2007 Holt, Rinehart and Winston Algebra 1 Book 51. This problem will prepare you for the Multi-Step Test Prep on page 364. a. Flora walks from her home to the bus stop at a rate of 50 steps per minute. Write a 5- 8 Slopes of Parallel and Perpendicular Lines 353 (2-5)B Writing Linear Equations - Parallel & Perp. 1. parallel 3. y = 3/4x - 1 & y - 3 = 3/4(x - 5) 5. y = 2/3x - 4 & y = - 3/2x + 2 ; y = -1 & x = 3 9. x = 7 & x = -9 ; y = -5/6x + 8 & y = -5/6x - 4 11. y = 3x + 2 & 3x + y = 27 ; y = 1/2x - 1 & -x + 2y = 17 13. y = 6x & y = -1/6x ; y = 1/6x & y = -6x 15. x - 6y = 15 & y = -6x - 8 ; y = 3x - 2 & 3y = -x - 11 17. 19. 21. 23. 25. 27. 29. 31. 33. 35. 37. 39. y = -6/7x neither parallel y = 1/2x - 5 y = 2x + 5 y = 3x + 13 y = -x + 5 y = 4x - 23 y = -3/4x y = -x + 1 y = 2/5x - 31/5 y = -1/5x - 11/5 41. 43. 45. 47. 49. 11/2/05 10:10:15 AM y = -1/2x - 1/2 y = 1/2x + 6 y=x-3 y=-4 Possible Answer: about - 4 354 a107se_c05_0349