SAT Question 606cdce7: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. An equation representing the linear relationship between $x$ and $y$ can be written in slope-intercept form $y=mx+b$, where $m$ is the slope of the graph of the equation in the xy-plane and $(0,b)$ is the y-intercept. The slope, $m$, can be calculated using two ordered pairs, $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, and the formula $m=\frac{y_2-y_1}{x_2-x_1}$. Substituting the ordered pairs $(-6,65)$ and $(6,29)$ from the table for $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, respectively, in this formula yields $m=\frac{29-65}{6-(-6)}$, which is equivalent to $m=\frac{-36}{12}$, or $m=-3$. Substituting $-3$ for $m$ in the formula $y=mx+b$ yields $y=-3x+b$. Substituting the point $(-6,65)$ into this equation yields $65=-3(-6)+b$, or $65=18+b$. Subtracting $18$ from both sides of this equation yields $47=b$. Substituting $47$ for $b$ in the equation $y=-3x+b$ yields $y=-3x+47$. Adding $3x$ to both sides of this equation yields $3x+y=47$. Multiplying both sides of this equation by $3$ yields $9x+3y=141$.