SAT Question d1f50dbe: Linear Functions answer and explanation with Desmos solution

Choice D is correct. It's given that $w$ represents the total fence area, in square feet. Since the fence will be stained twice, the amount of stain, in gallons, will need to cover $2w$ square feet. It's also given that one gallon of stain will cover $170$ square feet. Dividing the total area, in square feet, of the surface to be stained by the number of square feet covered by one gallon of stain gives the number of gallons of stain that will be needed. Dividing $2w$ by $170$ yields $\frac{2w}{170}$, or $\frac{w}{85}$. Therefore, the equation that represents the total amount of stain $S$, in gallons, needed to stain the fence of the yard twice is $S=\frac{w}{85}$.