sat-dog

Choice C is correct. An equation that defines a linear function $f$ can be written in the form $f\left(x\right)=mx+b$, where $m$ represents the slope and $b$ represents the y-intercept, $\left(0,b\right)$, of the line of $y=f\left(x\right)$ in the xy-plane. The function $f\left(x\right)=-5x+30$ is linear. Therefore, the graph of the given function $y=f\left(x\right)$ in the xy-plane has a y-intercept of $\left(0,30\right)$. It’s given that $f\left(x\right)$ gives the approximate volume, in fluid ounces, of juice Caleb had remaining after making $x$ popsicles. It follows that the y-intercept of $\left(0,30\right)$ means that Caleb had approximately $30$ fluid ounces of juice remaining after making $0$ popsicles. In other words, Caleb had approximately $30$ fluid ounces of juice when he began to make the popsicles.

Choice A is incorrect. This is an interpretation of the slope, rather than the y-intercept, of the graph of $y=f\left(x\right)$ in the xy-plane.

Choice B is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.