SAT Question b51c173d: Linear Functions answer and explanation with Desmos solution

Choice D is correct. An equation defining the linear function $f$ can be written in the form $f\left(x\right)=mx+b$, where $m$ is the slope and $\left(0,b\right)$ is the y-intercept of the graph of $y=f\left(x\right)$ in the xy-plane. It's given that the graph of $y=f\left(x\right)$ has a slope of $2$. Therefore, $m=2$. It's also given that the graph of $y=f\left(x\right)$ has a y-intercept at $\left(0,-5\right)$. Therefore, $b=-5$. Substituting $2$ for $m$ and $-5$ for $b$ in the equation $f\left(x\right)=mx+b$ yields $f\left(x\right)=2x-5$. Thus, the equation that defines $f$ is $f\left(x\right)=2x-5$.