See Problem 3.

For Exercises 15–18, are lines l 1 l sub 1  and l 2 l sub 2  perpendicular? Explain.

See Problem 4.

Write an equation of the line perpendicular to the given line that contains P.

19. P ( 6 , 6 ) ; y = 2 3 x p open 6 comma 6 close semicolon , y equals . 2 thirds , x
20. P ( 4 , 0 ) ; y = 1 2 x − 5 p open 4 comma 0 close semicolon , y equals . 1 half , x , minus 5
21. P ( 4 , 4 ) ; y = − 2 x − 8 p open 4 comma 4 close semicolon , y equals , minus 2 x minus 8

See Problem 5.

22. City Planning City planners want to construct a bike path perpendicular to Bruckner Boulevard at point P. An equation of the Bruckner Boulevard line is y = − 3 4 x . y equals , minus . 3 fourths , x .  Find an equation of the line for the bike path.

    

B Apply

Rewrite each equation in slope-intercept form, if necessary. Then determine whether the lines are parallel. Explain.

23. y = − x + 6 x + y = 20 table with 2 rows and 1 column , row1 column 1 , y equals negative x plus 6 , row2 column 1 , x plus y equals 20 , end table

24. y − 7 x = 6 y + 7 x = 8 table with 2 rows and 1 column , row1 column 1 , y minus 7 x equals 6 , row2 column 1 , y plus 7 x equals 8 , end table

25. 3 x + 4 y = 12 6 x + 2 y = 6 table with 2 rows and 1 column , row1 column 1 , 3 x plus 4 y equals 12 , row2 column 1 , 6 x plus 2 y equals 6 , end table

26. 2 x + 5 y = − 1 10 y = − 4 x − 20 table with 2 rows and 1 column , row1 column 1 , 2 x plus 5 y equals negative 1 , row2 column 1 , 10 y equals negative 4 x minus 20 , end table

27. Think About a Plan Line l 1 l sub 1  contains ( − 4 , 1 ) open negative 4 comma 1 close  and (2, 5) and line l 2 l sub 2  contains (3, 0) and ( − 3 , k ) . open negative 3 comma k close .  What value of k makes l 1 l sub 1  and l 2 l sub 2  parallel?
    • For l 1 l sub 1  and l 2 l sub 2  to be parallel, what must be true of their slopes?
    • What expressions represent the slopes of l 1 l sub 1  and l 2 ? l sub 2 , question mark
28. Open-Ended Write equations for two perpendicular lines that have the same y-intercept and do not pass through the origin.
29. Writing Can the y-intercepts of two nonvertical parallel lines be the same? Explain.

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