SAT Question 24854644: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice B is correct. The equation of a line in the xy-plane can be written in slope-intercept form $y=mx+b$, where $m$ is the slope of the line and $\left(0,b\right)$ is its y-intercept. It's given that the line passes through the point $\left(0,5\right)$. Therefore, $b=5$. It's also given that the line is parallel to the graph of $y=7x+4$, which means the line has the same slope as the graph of $y=7x+4$. The slope of the graph of $y=7x+4$ is $7$. Therefore, $m=7$. Substituting $7$ for $m$ and $5$ for $b$ in the equation $y=mx+b$ yields $y=7x+5$.