SAT Question 63be6c9a: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice C is correct. A line in the xy-plane can be represented by an equation of the form $y=mx+b$, where $m$ is the slope and $b$ is the y-coordinate of the y-intercept of the line. It's given that line $s$ passes through the point $\left(0,0\right)$. Therefore, the y-coordinate of the y-intercept of line $s$ is $0$. It's also given that line $s$ is parallel to the line represented by the equation $y=18x+2$. Since parallel lines have the same slope, it follows that the slope of line $s$ is $18$. Therefore, line $s$ can be represented by the equation $y=mx+b$, where $m=18$ and $b=0$. Substituting $18$ for $m$ and $0$ for $b$ in $y=mx+b$ yields the equation $y=18x+0$, or $y=18x$. If line $s$ passes through the point $\left(4,d\right)$, then when $x=4$, $y=d$ for the equation $y=18x$. Substituting $4$ for $x$ and $d$ for $y$ in this equation yields $d=18\left(4\right)$, or $d=72$.