sat suite question viewer

Algebra / Linear equations in two variables Difficulty: Medium

The graph models the relationship between the number of T-shirts, $x$ , and the number of sweatshirts, $y$ , that Kira can purchase for a school fundraiser. Which equation could represent this relationship?

$y = 7 x + 18$

$7 x + 18 y = 630$

$y = 18 x + 7$

$18 x + 7 y = 630$

Back question 126 of 126 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

Explanation

Choice B is correct. A line in the xy-plane can be written as $y = m x + b$ , where $m$ is the slope of the line and $b$ is the y-coordinate of the y-intercept. The graph shown is a line passing through the points $left parenthesis 0 comma 35 right parenthesis$ and $left parenthesis 90 comma 0 right parenthesis$ . Substituting $0$ for $x$ and $35$ for $y$ in the equation $y = m x + b$ yields $35 = m (0) + b$ , or $35 equals b$ . Substituting $35$ for $b$ , $90$ for $x$ , and $0$ for $y$ in the equation $y = m x + b$ yields $0 = 90 m + 35$ . Subtracting $35$ from both sides of this equation yields $- 35 = 90 m$ . Dividing both sides of this equation by $90$ yields $- \frac{35}{90} = m$ , or $- \frac{7}{18} = m$ . Substituting $- \frac{7}{18}$ for $m$ and $35$ for $b$ in the equation $y = m x + b$ yields $y = - \frac{7}{18} x + 35$ . Multiplying both sides of this equation by $18$ yields $18 y = - 7 x + 35 (18)$ , or $18 y = - 7 x + 630$ . Adding $7 x$ to both sides of this equation yields $7 x + 18 y = 630$ . Therefore, the equation $7 x + 18 y = 630$ represents the relationship between $x$ and $y$ modeled by the graph.

Choice A is incorrect. The point $left parenthesis 0 comma 35 right parenthesis$ is not on the graph of this equation, since $7 (0) + 18 = 18$ , not $35$ .

Choice C is incorrect. The point $left parenthesis 0 comma 35 right parenthesis$ is not on the graph of this equation, since $18 (0) + 7 = 7$ , not $35$ .

Choice D is incorrect. The point $left parenthesis 90 comma 0 right parenthesis$ is not on the graph of this equation, since $18 (90) + 7 (0) = 1,620$ , not $630$ .