SAT Question 8eb0e19e: Linear Functions answer and explanation with Desmos solution

Choice B is correct. A linear function can be defined by the equation $f\left(x\right)=mx+b$, 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. The slope of a line that passes through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ can be calculated using the equation $m=\frac{y_2-y_1}{x_2-x_1}$. The line shown passes through the points $\left(4,0\right)$ and $\left(0,8\right)$. Substituting $\left(4,0\right)$ for $\left(x_1,y_1\right)$ and $\left(0,8\right)$ for $\left(x_2,y_2\right)$ in the equation $m=\frac{y_2-y_1}{x_2-x_1}$ yields $m=\frac{8-0}{0-4}$, or $m=-2$. Since the line shown passes through the point $\left(0,8\right)$, it follows that $b=8$. Substituting $-2$ for $m$ and $8$ for $b$ in the equation $f\left(x\right)=mx+b$ yields $f\left(x\right)=-2x+8$. Therefore, the equation $f\left(x\right)=-2x+8$ defines function $f$.