SAT Question e103300e: Linear Functions answer and explanation with Desmos solution

Choice A is correct. It's given that the function $f(x)$ is defined as $19$ more than $4$ times a number $x$. This can be represented by the equation $f(x)=4x+19$. The x-intercept of the graph of $y=f(x)$ in the xy-plane is the point where the graph intersects the x-axis, or the point on the graph where the value of $f(x)$ is equal to $0$. Substituting $0$ for $f(x)$ in the equation $f(x)=4x+19$ yields $0=4x+19$. Subtracting $19$ from each side of this equation yields $-19=4x$. Dividing each side of this equation by $4$ yields $x=-\frac{19}{4}$. Therefore, when $f(x)=0$, the number is $-\frac{19}{4}$.