SAT Question d7c8ba0b: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. An equation defining a line in the xy-plane can be written in the form $y=mx+b$, where $m$ represents the slope and $\left(0,b\right)$ represents the y-intercept of the line. It's given that line $t$ passes through the point $\left(0,9\right)$; therefore, $b=9$. The slope, $m$, of a line can be found using any two points on the line, $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, and the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Substituting $\left(0,9\right)$ and $\left(1,17\right)$ for $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, respectively, in the slope formula yields $m=\frac{17-9}{1-0}$, or $m=8$. Substituting $8$ for $m$ and $9$ for $b$ in the equation $y=mx+b$ yields $y=8x+9$.