SAT Question ba79f10f: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. A linear relationship can be represented by an equation of the form $y=mx+b$, where $m$ and $b$ are constants. It's given in the table that when $x=0$, $y=18$. Substituting $0$ for $x$ and $18$ for $y$ in $y=mx+b$ yields $18=m\left(0\right)+b$, or $18=b$. Substituting $18$ for $b$ in the equation $y=mx+b$ yields $y=mx+18$. It's also given in the table that when $x=1$, $y=13$. Substituting $1$ for $x$ and $13$ for $y$ in the equation $y=mx+18$ yields $13=m\left(1\right)+18$, or $13=m+18$. Subtracting $18$ from both sides of this equation yields $-5=m$. Therefore, the equation $y=-5x+18$ represents the relationship between $x$ and $y$.