SAT Question 78391fcc: Linear Functions answer and explanation with Desmos solution

Choice B is correct. The equation of a linear function can be written in the form $y=mx+b$, where $y=f(x)$, $m$ is the slope of the graph of $y=f(x)$, and $b$ is the $y$-coordinate of the $y$-intercept of the graph. The value of $m$ can be found using the slope formula, $m=\frac{y_2-y_1}{x_2-x_1}$. According to the table, the points $(-11,21)$ and $(-10,18)$ lie on the graph of $y=f(x)$. Using these two points in the slope formula yields $m=\frac{18-21}{-10+11}$, or $-3$. Substituting $-3$ for $m$ in the slope-intercept form of the equation yields $y=-3x+b$. The value of $b$ can be found by substituting values from the table and solving; for example, substituting the coordinates of the point $(-11,21)$ into the equation $y=-3x+b$ gives $21=-3\times -11+b$, which yields $b=-12$. This means the function given by the table can be represented by the equation $y=-3x-12$. The value of the $x$-intercept of the graph of $y=f(x)$ can be determined by finding the value of $x$ when $y=0$. Substituting $y=0$ into $y=-3x-12$ yields $0=-3x-12$, or $x=-4$. This corresponds to the point $(-4,0)$.