SAT Question 5b7599a6: Linear Equations In Two Variables answer and explanation with Desmos solution

Choice C is correct. The equation representing the linear relationship shown can be written in slope-intercept form $y=mx+b$, where $m$ is the slope and $\left(0,b\right)$ is the y-intercept of the line. The line shown passes through the points $\left(0,6\right)$ and $\left(2,0\right)$. Given two points on a line, $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, the slope of the line can be calculated using the equation $m=\frac{y_2-y_1}{x_2-x_1}$. Substituting $\left(0,6\right)$ and $\left(2,0\right)$ for $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$, respectively, in this equation yields $m=\frac{0-6}{2-0}$, which is equivalent to $m=-\frac{6}{2}$, or $m=-3$. Since $\left(0,6\right)$ is the y-intercept, it follows that $b=6$. Substituting $-3$ for $m$ and $6$ for $b$ in the equation $y=mx+b$ yields $y=-3x+6$. Adding $3x$ to both sides of this equation yields $3x+y=6$. Multiplying this equation by $6$ yields $18x+6y=36$. It follows that the equation $18x+Ry=36$, where $R$ is a positive constant, represents this relationship.