Did You Find a Parking Space?
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1 Lesson.4 Skills Practice Name Date Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane Vocabulary Complete the sentence. 1. The point-slope form of the equation of the line that passes through (x 1, y 1 ) and has slope m is. Problem Set Determine whether each pair of lines are parallel, perpendicular, or neither. Explain your reasoning. 1. line n: y x 4 line m: y x 1 8 Parallel. The slope of line n is, which is equal to the slope of line m, so the lines are parallel.. line p: y 3x 1 line q: y 1 3 x 1 0 Carnegie Learning 3. line r: y x 1 line s: y 1 x 6 4. line n: y 6x 1 line m: y 6x Chapter Skills Practice 613
2 Lesson.4 Skills Practice page. line p: y x 4 line q: x 1 y 8 6. line r: y 1 x 6 line s: 3x 1 6y Determine whether the lines shown on each coordinate plane are parallel, perpendicular, or neither. Explain your reasoning. 7. y 9 (8, 9) (0, 8) 8 7 p q (9, ) 1 (, 0) x The lines 3 3 are perpendicular. The slope of line p is and the slope of line q is 3. Because 3 ) 1, the lines are perpendicular. ( 0 Carnegie Learning 614 Chapter Skills Practice
3 Lesson.4 Skills Practice page 3 Name Date 8. 9 y (1, 10) (8, 10) s r (3, 0) (6, 0) x 9. y 9 (7, 9) 8 7 (10, 8) 6 t u 0 Carnegie Learning (1, 0) (6, 0) x Chapter Skills Practice 61
4 Lesson.4 Skills Practice page y 9 (8, 9) I (10, 6) 4 3 (0, 3) m 1 (, 0) x 11. y (, 10) 9 8 (0, 8) s (3, 4) t (9, 1) x 0 Carnegie Learning 616 Chapter Skills Practice
5 Lesson.4 Skills Practice page Name Date. y (0, ) m (8, 9) (4, 7) n (6, 3) x Determine an equation for each parallel line described. Write your answer in both point-slope form and slope-intercept form. 0 Carnegie Learning 13. What is the equation of a line 4 parallel to y 4 x 1 that passes through (1, )? Point-slope form: (y ) (x 1) Slope-intercept 4 form: y x 4 4 y x y x What is the equation of a line parallel to y x 1 3 that passes through (3, 1)? Chapter Skills Practice 617
6 Lesson.4 Skills Practice page 6 1. What is the equation of a line parallel to y 7x 8 that passes through (, )? 16. What is the equation of a line parallel to y 1 x 1 6 that passes through (4, 1)? 17. What is the equation of a line parallel to y 1 x 4 that passes through (9, 8)? 3 0 Carnegie Learning 618 Chapter Skills Practice
7 Lesson.4 Skills Practice page 7 Name Date 18. What is the equation of a line parallel to y 4x 7 that passes through (, 9)? Determine an equation for each perpendicular line described. Write your answer in both point-slope form and slope-intercept form. 19. What is the equation of a line perpendicular 1 to y x 6 that passes through (, 4)? The slope of the new line must 1 be. Point-slope form: (y 4) (x ) Slope-intercept 1 form: y 4 x 1 1 y 1 x y x What is the equation of a line perpendicular to y 3x 1 4 that passes through (1, 6)? 0 Carnegie Learning Chapter Skills Practice 619
8 Lesson.4 Skills Practice page 8 1. What is the equation of a line perpendicular to y x 1 that passes through (, 8)?. What is the equation of a line perpendicular to y 3 x 1 that passes through (, 3)? 4 3. What is the equation of a line perpendicular to y 6x that passes through (6, 3)? 4. What is the equation of a line perpendicular to y x 1 that passes through (1, 4)? 0 Carnegie Learning 60 Chapter Skills Practice
9 Lesson.4 Skills Practice page 9 Name Date Determine the equation of a vertical line that passes through each given point.. (, 1) 6. (3, 1) x 7. (9, 7) 8. (11, 8) 9. (, 10) 30. (0, 4) Determine the equation of a horizontal line that passes through each given point. 31. (4, 7) 3. (6, ) y (8, 3) 34. (, 9) 3. (7, 8) 36. (6, ) 0 Carnegie Learning Chapter Skills Practice 61
10 Lesson.4 Skills Practice page 10 Calculate the distance from each given point to the given line. 37. Point: (0, 4); Line: f(x) x 3 Write the equation for the line perpendicular to the given line that goes 1 through the given point. Since the slope of f is, the slope of the perpendicular segment is. y mx 1 1 b 4 (0) 1 b 4 b 1 The equation of the line containing the perpendicular segment is y x 1 4. Calculate 1 the point of intersection of the segment and the line f(x) x 3. x 1 4 x 3 x 1 8 4x 6 x 14 x y (.8) The point of intersection is (.8,.6). Calculate the distance. d (0.8 ) 1 (4.6 ) d (.8 ) 1 (1.4 ) d d The distance from the point (0, 4) to the line f(x) x 3 is approximately 3.13 units. 0 Carnegie Learning 6 Chapter Skills Practice
11 Lesson.4 Skills Practice page 11 Name Date 38. Point: (1, 3); Line: f(x) 1 x 4 Write the equation for the line perpendicular to the given line that goes through the given point. 0 Carnegie Learning Chapter Skills Practice 63
12 Lesson.4 Skills Practice page 39. Point: (, ); Line: f(x) 3 x 1 6 Write the equation for the line perpendicular to the given line that goes through the given point. 0 Carnegie Learning 64 Chapter Skills Practice
13 Lesson.4 Skills Practice page 13 Name Date 40. Point: (1, ); Line: f(x) 4x 1 11 Write the equation for the line perpendicular to the given line that goes through the given point. 0 Carnegie Learning Chapter Skills Practice 6
14 Lesson.4 Skills Practice page Point: (3, 1); Line: f(x) 1 3 x 6 Write the equation for the line perpendicular to the given line that goes through the given point. 0 Carnegie Learning 66 Chapter Skills Practice
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