B Apply

Graph each equation.

36. 3 x + 5 y = 12 3 x plus 5 y equals 12
37. 2 x + y = 3 2 x plus y equals 3
38. 6 y − 4 x = − 24 6 y minus 4 x equals negative 24
39. 3 y − x = − 6 3 y minus x equals negative 6
40. − 20 x − 45 y = 48 negative 20 x minus 45 y equals 48
41. 2 x − 3 2 y = − 3 2 x minus , 3 halves , y equals negative 3

Write an equation of the line through each pair of points. Use point-slope form.

42. ( 3 2 , − 1 2 )  and  ( − 2 3 , 1 3 ) open . 3 halves , comma negative , 1 half . close . and . open . negative , 2 thirds , comma , 1 third . close
43. ( − 1 2 , − 1 2 ) open . negative , 1 half , comma negative , 1 half . close  and ( − 2 , − 4 ) open negative 2 comma negative 4 close
44. ( 0 , 1 2 )  and  ( 5 7 , 0 ) open . 0 comma , 1 half . close . and . open . 5 sevenths , comma 0 . close

45. Think About a Plan Write an equation for the line shown here. Each interval is 1 unit.

    

    • What do you know from the graph?
    • Which form of the equation of a line could you use with the information you have?

Write an equation for each line. Each interval is 1 unit.

Find the slope, if any, and the intercepts, if any, of each line.

48. f ( x ) = 2 3 x + 4 f open x close equals , 2 thirds , x plus 4
49. y = − x + 1000 y equals negative x plus , 1000
50. y + 0.8 x = 0.4 y plus 0.8 x equals 0.4
51. g ( x ) = 54 x − 1 g open x close equals 54 x minus 1
52. x + 3 = 0 x plus 3 equals 0
53. y + 3 = 3 y plus 3 equals 3
54. 1. Write the point-slope form of the line that passes through A ( − 3 , 12 ) eh open negative 3 comma 12 close  and B ( 9 , − 4 ) . b open 9 comma negative 4 close .  Use point A in the equation.
    2. Write the point-slope form of the same line using point B in the equation.
    3. Rewrite each equation in standard form. What do you notice?

Write an equation for each line. Then graph the line.

55. m = 0 , m equals 0 comma  through ( 5 , − 1 ) open 5 comma negative 1 close
56. m = 5 6 , m equals , 5 sixths , comma  through ( − 2 , 0 ) open negative 2 comma 0 close
57. m = − 3 2 , m equals negative , 3 halves , comma  through ( 0 , − 1 ) open 0 comma negative 1 close

58. Reasoning Suppose lines ℓ 1 script l sub 1  and ℓ 2 script l sub 2  intersect at the origin. Also, ℓ 1 script l sub 1  has slope y x ( x > 0 , y > 0 ) y over x , open x greater than 0 comma y greater than 0 close  and ℓ 2 script l sub 2  has slope − x y . negative , x over y , .  Then ℓ 1 script l sub 1  contains (x, y) and ℓ 2 script l sub 2  contains ( − y , x ) . open negative y comma x close .

    
    Image Long Description

    1. Explain why the two right triangles are congruent.

    2. Complete each equation about the angle measures a, b, c, and d.

       a = □ eh equals white square	c = □ c equals white square
       a + c = □ c equals white square	b + d = □ d equals white square

    3. What must be true about a + b? Why?
    4. What must be true about ℓ 1 script l sub 1  and ℓ 2 ? script l sub 2 , question mark  Why?

Table of Contents