Linear equations in two variables SAT question

Choice C is correct. It's given from the graph that the points $(0,7)$ and $(8,0)$ lie on the line. For two points on a line, $(x_1,y_1)$ and $(x_2,y_2)$, the slope of the line can be calculated using the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Substituting $(0,7)$ for $(x_1,y_1)$ and $(8,0)$ for $(x_2,y_2)$ in this formula, the slope of the line can be calculated as $m=\frac{0-7}{8-0}$, or $m=-\frac{7}{8}$. It's also given that the point $(d,4)$ lies on the line. Substituting $(d,4)$ for $(x_1,y_1)$, $(8,0)$ for $(x_2,y_2)$, and $-\frac{7}{8}$ for $m$ in the slope formula yields $-\frac{7}{8}=\frac{0-4}{8-d}$, or $-\frac{7}{8}=\frac{-4}{8-d}$. Multiplying both sides of this equation by $8-d$ yields $-\frac{7}{8}(8-d)=-4$. Expanding the left-hand side of this equation yields $-7+\frac{7}{8}d=-4$. Adding $7$ to both sides of this equation yields $\frac{7}{8}d=3$. Multiplying both sides of this equation by $\frac{8}{7}$ yields $d=\frac{24}{7}$. Thus, the value of $d$ is $\frac{24}{7}$.

Choice A is incorrect. This is the value of $y$ when $x=4$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.