SAT Question d62ad380: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice C is correct. The relationship between $s$ and $P$ can be modeled by a linear equation of the form $P=ks+a$, where $k$ and $a$ are constants. The table shows that $P$ increases by $10$ when $s$ increases by $3$, so $k=\frac{10}{3}$. To solve for $a$, substitute one of the given pairs of values for $s$ and $P$: when $s=3$, $P=8$, so $8=\frac{10}{3}\times 3+a$, which yields $a=-2$. The solution is therefore $P=\frac{10}{3}s-2$.