Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.

7. ( 1 , 3 ) ; y = 3 x + 2 open 1 comma 3 close semicolon y equals 3 x plus 2
8. ( 2 , − 2 ) ; y = − x − 2 open 2 comma negative 2 close semicolon y equals negative x minus 2
9. ( 1 , − 3 ) ; y + 2 = 4 ( x − 1 ) open 1 comma negative 3 close semicolon y plus 2 equals 4 open x minus 1 close
10. ( 2 , − 1 ) ; y = − 3 2 x + 6 open 2 comma negative 1 close semicolon y equals , negative , 3 halves , x plus 6
11. ( 0 , 0 ) ; y = 2 3 x + 1 open 0 comma 0 close semicolon y equals , 2 thirds , x plus 1
12. ( 4 , 2 ) ; x = − 3 open 4 comma 2 close semicolon x equals negative 3

See Problem 2.

Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain.

13. y = x + 11 y equals x plus 11

    y = − x + 2 y equals negative x plus 2

14. y = 3 4 x − 1 y equals , 3 fourths , x minus 1

    y = 3 4 x + 29 y equals , 3 fourths , x plus 29

15. y = − 2 x + 3 y equals negative 2 x plus 3

    2 x + y = 7 2 x plus y equals 7

16. y − 4 = 3 ( x + 2 ) y minus 4 equals 3 open x plus 2 close

    2 x + 6 y = 10 2 x plus 6 y equals 10

17. y = − 7 y equals negative 7

    x = 2 x equals 2

18. y = 4 x − 2 y equals 4 x minus 2

    − x + 4 y = 0 negative x plus 4 y equals 0

See Problem 3.

Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.

19. ( 0 , 0 ) ; y = − 3 x + 2 open 0 comma 0 close semicolon y equals negative 3 x plus 2
20. ( − 2 , 3 ) ; y = 1 2 x − 1 open negative 2 comma 3 close semicolon y equals , 1 half , x minus 1
21. ( 1 , − 2 ) ; y = 5 x + 4 open 1 comma negative 2 close semicolon y equals 5 x plus 4
22. ( − 3 , 2 ) ; x − 2 y = 7 open negative 3 comma 2 close semicolon x minus 2 y equals 7
23. ( 5 , 0 ) ; y + 1 = 2 ( x − 3 ) open 5 comma 0 close semicolon y plus 1 equals 2 open x minus 3 close
24. ( 1 , − 6 ) ; x − 2 y = 4 open 1 comma negative 6 close semicolon x minus 2 y equals 4

    See Problem 4.

25. Urban Planning A path for a new city park will connect the park entrance to Main Street. The path should be perpendicular to Main Street. What is an equation that represents the path?

    

26. Bike Path A bike path is being planned for the park in Exercise 25. The bike path will be parallel to Main Street and will pass through the park entrance. What is an equation of the line that represents the bike path?

B Apply

27. Identify each pair of parallel lines. Then identify each pair of perpendicular lines.

    line a : y = 3 x + 3 eh colon y equals 3 x plus 3	line b : x = − 1 b colon x equals negative 1	line c : y − 5 = 1 2 ( x − 2 ) c colon y minus 5 equals , 1 half , open x minus 2 close
    line d : y = 3 d colon y equals 3	line e : y + 4 = − 2 ( x + 6 ) e colon y plus 4 equals negative 2 open x plus 6 close	line f : 9 x − 3 y = 5 f colon 9 x minus 3 y equals 5

Determine whether each statement is always, sometimes, or never true. Explain.

28. A horizontal line is parallel to the x-axis.
29. Two lines with positive slopes are parallel.
30. Two lines with the same slope and different y-intercepts are perpendicular.
31. Open-Ended What is an equation of a line that is parallel to the x-axis? What is an equation of a line that is parallel to the y-axis?
32. Error Analysis A student says that the graph of y = 1 3 x + 1 y equals , 1 third , x plus 1  is parallel to the graph of y = − 3 x + 4 . y equals negative 3 x plus 4 .  Describe and correct the student's error.

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