SAT Question 6fa1dc0f: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. A line in the xy-plane with a slope of $m$ and a y-intercept of $\left(0,b\right)$ can be defined by an equation in the form $y=mx+b$. It's given that line $r$ has a slope of $4$ and passes through the point $\left(0,6\right)$. It follows that $m=4$ and $b=6$. Substituting $4$ for $m$ and $6$ for $b$ in the equation $y=mx+b$ yields $y=4x+6$. Therefore, the equation $y=4x+6$ defines line $r$.