SAT Question fc4a0d2a: Linear Functions answer and explanation with Desmos solution

Choice A is correct. It's given that $g(x)=3(14x-15)$. Substituting $3\left(14x-15\right)$ for $g(x)$ in the equation $y=g(x)-2$ yields $y=3(14x-15)-2$. The y-intercept of the graph of a function in the xy-plane is the point where the function crosses the y-axis, which occurs when $x=0$. Substituting $0$ for $x$ in the equation $y=3(14x-15)-2$ yields $y=3(14(0)-15)-2$. It follows that $y=-45-2$, or $y=-47$. Therefore, the y-intercept of the graph of $y=g(x)-2$ in the xy-plane is $(0,-47)$, and the y-coordinate of the y-intercept of the graph is $-47$.