b. Juan’s Workout 0 10 20 40 80 120 160 Time (min) Calories burned c. The graph forms a line. 55. No; each constant change in time (+1 s) is not accompanied by a constant change in height. 56. Yes; the equation can be written in standard form with A = 1, B = 0, and C = 9. No; all solutions are ordered pairs with x-value 9. The x-value 9 corresponds to more than one y-value. TEST PREP 57. C; C is not linear, because x appears in the denominator of a fraction. 58. G; Each second, sound will move 331 meters. So the distance covered is 331 times the number of seconds. 59. Possible answer: 3x + 2y = 7; it is a linear equation because it can be written in standard form with A = 3, B = 2, and C = 7. A table of values also shows it is a linear function: x y -3 8 -2 6.5 -1 5 0 3.5 1 2 2 0.5 Each constant change in x (+1) is accompanied by a constant change in y (-1.5). The graph shows a linear function. 2 4 x y 0 2 -2 Both the graph and the table show solutions to the equation. CHALLENGE AND EXTEND 60. y = 0; x = 0; the first describes a linear function, but the second does not. 61. Perimeter of a Square Side Length Perimeter 1 4 2 8 3 12 4 16 62. Area of a Square Side Length Area 1 1 2 4 3 9 4 16 linear not linear 63. Volume of a Cube Side Length Volume 1 1 2 8 3 27 4 64 not linear USING INTERCEPTS CHECK IT OUT! 1a. The y-intercept is 3. The x-intercept is -2. b. -3x + 5y = 30 -3x + 5(0) = 30 -3x + 0 = 30 -3x = 30 -3x _ -3 = 30 _ -3 x = -10 The x-intercept is -10. -3x + 5y = 30 -3(0) + 5y = 30 0 + 5y = 30 5y = 30 5y _ 5 = 30 _ 5 y = 6 The y-intercept is 6. c. 4x + 2y = 16 4x + 2(0) = 16 4x + 0 = 16 4x = 16 4x _ 4 = 16 _ 4 x = 4 The x-intercept is 4. 4x + 2y = 16 4(0) + 2y = 16 0 + 2y = 16 2y = 16 2y _ 2 = 16 _ 2 y = 8 The y-intercept is 8. 2a. 2x + 3y = 60 ________ -2x ____ -2x 3y = 60 - 2x 3y _ 3 = 60 - 2x _ 3 y = 20 - 2 _ 3 x x 0 6 15 24 30 y = 20 - 2 _ 3 x 20 16 10 4 0 School Store Purchases 0 10 20 30 10 20 Pens Notebooks The x-intercept is 30. The y-intercept is 20. 109 Holt McDougal Algebra 1 4-2
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b.
Juan’s Workout
0 10 20
40
80
120
160
Time (min)
Calo
ries
bur
ned
c. The graph forms a line.
55. No; each constant change in time (+1 s) is not accompanied by a constant change in height.
56. Yes; the equation can be written in standard form with A = 1, B = 0, and C = 9. No; all solutions are ordered pairs with x-value 9. The x-value 9 corresponds to more than one y-value.
teSt prep
57. C; C is not linear, because x appears in the denominator of a fraction.
58. G; Each second, sound will move 331 meters. So the distance covered is 331 times the number of seconds.
59. Possible answer: 3x + 2y = 7; it is a linear equation because it can be written in standard form with A = 3, B = 2, and C = 7.
A table of values also shows it is a linear function:
x y
-3 8
-2 6.5
-1 5
0 3.5
1 2
2 0.5
Each constant change in x (+1) is accompanied by a constant change in y (-1.5).
The graph shows a linear function.
2
4
x
y
0 2-2
Both the graph and the table show solutions to the equation.
challenge and extend
60. y = 0; x = 0; the first describes a linear function, but the second does not.
Possible answer: scale on the x-axis should include numbers from 0 to a number a little greater than 950; scale on y-axis should include numbers from a little less than -55 to 0.