SAT Question 30281058: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. It's given that the graph of $y=x^2-9$ and line $p$ intersect at $(1,a)$ and $(5,b)$. Therefore, the value of $y$ when $x=1$ is the value of $a$, and the value of $y$ when $x=5$ is the value of $b$. Substituting $1$ for $x$ in the given equation yields $y=1^2-9$, or $y=-8$. Similarly, substituting $5$ for $x$ in the given equation yields $y=5^2-9$, or $y=16$. Therefore, the intersection points are $(1,-8)$ and $(5,16)$. The slope of line $p$ is the ratio of the change in $y$ to the change in $x$ between these two points: $\frac{16-(-8)}{5-1}=\frac{24}{4}$, or $6$.