SAT Question e470e19d: Linear Functions answer and explanation with Desmos solution

Choice D is correct. The given function $f$ is a linear function. Therefore, the graph of $y=f\left(x\right)$ in the xy-plane has one x-intercept at the point $\left(k,0\right)$, where $k$ is a constant. Substituting $0$ for $f\left(x\right)$ and $k$ for $x$ in the given function yields $0=7k-84$. Adding $84$ to both sides of this equation yields $84=7k$. Dividing both sides of this equation by $7$ yields $12=k$. Therefore, the x-intercept of the graph of $y=f\left(x\right)$ in the xy-plane is $\left(12,0\right)$.