sat-dog

Choice B is correct. The graph shown is a line passing through the points $\left(0,40\right)$ and $\left(60,0\right)$. 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, $8x+12y=480$, yields $8\left(0\right)+12\left(40\right)=480$, or $480=480$, which is true. Substituting $60$ for $x$ and $0$ for $y$ in the equation $8x+12y=480$ yields $8\left(60\right)+12\left(0\right)=480$, or $480=480$, which is true. Therefore, the equation $8x+12y=480$ represents the relationship between $x$ and $y$.

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

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

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