SAT Question 4722abd2: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice C is correct. It’s given that line $p$ is defined by the equation $2y+8x=11$. The equation can be written in slope-intercept form $y=mx+b$, where $m$ represents the slope of the line. Subtracting $8x$ from both sides of the equation $2y+8x=11$ yields $2y=-8x+11$. Dividing both sides of this equation by $2$ yields $y=-4x+\frac{11}{2}$. Therefore, the slope of line $p$ in the xy-plane is $-4$. It's also given that line $p$ is perpendicular to line $r$. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of line $r$ is $-\frac{1}{\left(-4\right)}=\frac{1}{4}$.