SAT Question c387583f: Linear Functions answer and explanation with Desmos solution

For a linear equation in the form $y=mx+b$, $m$ represents the slope and $b$ represents the y-coordinate of the y-intercept of the graph in the xy-plane. The slope of the graph of a line containing any two points, $(x_1,y_1)$ and $(x_2,y_2)$, can be found using the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. It’s given that in the xy-plane, line $k$ passes through the points $(8,6)$ and $(9,12)$. Substituting $(8,6)$ and $(9,12)$ for $(x_1,y_1)$ and $(x_2,y_2)$, respectively, in the slope formula yields $m=\frac{12-6}{9-8}$, or $m=6$. Since line $k$ passes through the point $(9,12)$ and the slope of the line is $6$, substituting $9$ for $x$, $12$ for $y$, and $6$ for $m$ in the equation $y=mx+b$ yields $12=(6)(9)+b$, or $12=54+b$. Subtracting $54$ from both sides of this equation yields $-42=b$. Therefore, the value of $b$ is $-42$.