Linear functions SAT question

Choice B is correct. An equation defining a linear function can be written in the form $f(x)=mx+b$, where $m$ and $b$ are constants, $m$ is the slope of the graph of $y=f(x)$ in the xy-plane, and $(0,b)$ is the y-intercept of the graph. It's given that for the function $f$, the graph of $y=f(x)$ in the xy-plane has a slope of $3$. Therefore, $m=3$. It's also given that this graph passes through the point $(0,-8)$. Therefore, the y-intercept of the graph is $(0,-8)$, and it follows that $b=-8$. Substituting $3$ for $m$ and $-8$ for $b$ in the equation $f(x)=mx+b$ yields $f(x)=3x-8$. Thus, the equation that defines $f$ is $f(x)=3x-8$.

Choice A is incorrect. For this function, the graph of $y=f(x)$ in the xy-plane passes through the point $(0,0)$, not $(0,-8)$.

Choice C is incorrect. For this function, the graph of $y=f(x)$ in the xy-plane passes through the point $(0,5)$, not $(0,-8)$.

Choice D is incorrect. For this function, the graph of $y=f(x)$ in the xy-plane passes through the point $(0,11)$, not $(0,-8)$.