SAT Question 2eef7e61: Linear Functions answer and explanation with Desmos solution

Choice B is correct. The equation for the function $f$ in the $xy$-plane can be represented by $f(x)=mx+b$, where $m$ is the slope and $b$ is the $y$-coordinate of the $y$-intercept. Since it's given that the line has a slope of $\frac{3}{4}$, it follows that $m=\frac{3}{4}$ in $f(x)=mx+b$, which yields $y=\frac{3}{4}x+b$. It's given that $f(0)=3$. This implies that the graph of the function $f$ in the $xy$-plane passes through the point $(0,3)$. Thus, the $y$-coordinate of the $y$-intercept of the graph is $3$, so $b=3$ in $f(x)=\frac{3}{4}x+b$, which yields $f(x)=\frac{3}{4}x+3$. Therefore, the equation $f(x)=\frac{3}{4}x+3$ defines the function $f$.