33. Think About a Plan A designer is creating a new logo, as shown below. The designer wants to add a line to the logo that will be perpendicular to the blue line and pass through the red point. What equation represents the new line?

    • What is the slope of the blue line?

    • What is the slope of the new line?

      

34. Reasoning For what value of k are the graphs of 12 y = − 3 x + 8 12 y equals negative 3 x plus 8  and 6 y = k x − 5 6 y equals k x minus 5  parallel? For what value of k are they perpendicular?
35. Agriculture Two farmers use combines to harvest corn from their fields. One farmer has 600 acres of corn, and the other has 1000 acres of corn. Each farmer's combine can harvest 100 acres per day. Write two equations for the number of acres y of corn not harvested after x days. Are the graphs of the equations parallel, perpendicular, or neither? How do you know?

C Challenge

36. Geometry In a rectangle, opposite sides are parallel and adjacent sides are perpendicular. Figure ABCD has vertices A ( − 3 , 3 ) , B ( − 1 , − 2 ) , C ( 4 , 0 ) , eh open negative 3 comma 3 close comma b open negative 1 comma negative 2 close comma c open 4 comma 0 close comma  and D ( 2 , 5 ) . d open 2 comma 5 close .  Show that ABCD is a rectangle.
37. Geometry A right triangle has two sides that are perpendicular to each other. Triangle PQR has vertices P(4, 3), Q ( 2 , − 1 ) , q open 2 comma negative 1 close comma  and R(0, 1). Determine whether PQR is a right triangle. Explain your reasoning.

Standardized Test Prep

SAT/ACT

38. Which equation represents the graph of a line parallel to the line below?

    

    1. y = 1 2 x + 5 y equals , 1 half , x plus 5
    2. y = 2 x − 6 y equals 2 x minus 6
    3. y = − 2 x + 4 y equals negative 2 x plus 4
    4. y = − 1 2 x − 2 y equals , negative , 1 half , x minus 2

39. What is the solution of ( 5 x − 1 ) + ( − 2 x + 7 ) = 9 ? open 5 x minus 1 close plus open negative 2 x plus 7 close equals 9 question mark

    6. 3 7 3 sevenths
    7. 1
    8. 3
    9. 5

Short Response

40. Sal's Supermarket sells cases of twenty-four 12-oz bottles of water for $15.50. Shopper's World sells 12-packs of 12-oz bottles of water for $8.15. Which store has the better price per bottle? Explain.

Mixed Review

See Lesson 5-5.

Graph each equation using x- and y-intercepts.

41. x + y = 8 x plus y equals 8
42. 2 x + y = − 3 2 x plus y equals negative 3
43. x − 3 y = − 6 x minus 3 y equals negative 6

Get Ready! To prepare for Lesson 5-7, do Exercises 44–47.

See Lesson 5-3.

Write an equation in slope-intercept form of the line that passes through the given points.

44. (1, 1), (3, 7)
45. (2, 5), (12, 1)
46. (0.5, 2), (4.5, 3)
47. (13, 20), (6, 60)

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