SAT Question c39dbbdf: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice B is correct. It's given that line $s$ is parallel to line $r$ in the xy-plane. This means that the slope of line $r$ is equal to the slope of line $s$. Line $r$ is defined by the equation $4x-9y=3$. This equation can be written in slope-intercept form $y=mx+b$, where $m$ represents the slope of the line and $b$ represents the y-coordinate of the y-intercept of the line. Subtracting $4x$ from both sides of the equation $4x-9y=3$ yields $-9y=-4x+3$. Dividing both sides of this equation by $-9$ yields $y=\frac{4}{9}x-\frac{1}{3}$. Therefore, the slope of line $r$ is $\frac{4}{9}$. Since parallel lines have equal slopes, the slope of line $s$ is also $\frac{4}{9}$.