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Algebra / Linear equations in two variables Difficulty: Medium

The graph shows the relationship between the number of shares of stock from Company A, $x$ , and the number of shares of stock from Company B, $y$ , that Simone can purchase. Which equation could represent this relationship?

$y = 8 x + 12$

$8 x + 12 y = 480$

$y = 12 x + 8$

$12 x + 8 y = 480$

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Explanation

Choice B is correct. The graph shown is a line passing through the points $left parenthesis 0 comma 40 right parenthesis$ and $left parenthesis 60 comma 0 right parenthesis$ . Since the relationship between $x$ and $y$ is linear, if two points on the graph make a linear equation true, then the equation represents the relationship. Substituting $0$ for $x$ and $40$ for $y$ in the equation in choice B, $8 x + 12 y = 480$ , yields $8 (0) + 12 (40) = 480$ , or $480 equals 480$ , which is true. Substituting $60$ for $x$ and $0$ for $y$ in the equation $8 x + 12 y = 480$ yields $8 (60) + 12 (0) = 480$ , or $480 equals 480$ , which is true. Therefore, the equation $8 x + 12 y = 480$ represents the relationship between $x$ and $y$ .

Choice A is incorrect. The point $left parenthesis 0 comma 40 right parenthesis$ is not on the graph of this equation, since $40 = 8 (0) + 12$ , or $40 equals 12$ , is not true.

Choice C is incorrect. The point $left parenthesis 0 comma 40 right parenthesis$ is not on the graph of this equation, since $40 = 12 (0) + 8$ , or $40 equals 8$ , is not true.

Choice D is incorrect. The point $left parenthesis 0 comma 40 right parenthesis$ is not on the graph of this equation, since $12 (0) + 8 (40) = 480$ , or $320 equals 480$ , is not true.