SAT Question 1993561d: Linear Functions answer and explanation with Desmos solution

Choice A is correct. An equation that defines a linear function $f$ can be written in the form $f(x)=mx+b$, where $m$ 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 linear function $f$, the graph of $y=f(x)$ in the xy-plane has a slope of $\frac{1}{4}$. Therefore, $m=\frac{1}{4}$. It’s also given that the graph of $y=f(x)$ passes through the point $(0,5)$. Therefore, the y-intercept of the graph is $(0,5)$, and it follows that $b=5$. Substituting $\frac{1}{4}$ for $m$ and $5$ for $b$ in the equation $f(x)=mx+b$ yields $f(x)=\frac{1}{4}x+5$.