SAT Question 114ae8a9: Linear Functions answer and explanation with Desmos solution

Choice B is correct. It’s given that a train traveled $173$ miles in the first $3$ hours of a trip. It's also given that the train traveled at an average speed of $53$ miles per hour for the remainder of the trip. Since the trip was $x$ hours long, it follows that the remainder of the trip was $x-3$ hours. Therefore, $53(x-3)$ represents the distance, in miles, the train traveled for the remainder of the trip. Adding $173$ to $53(x-3)$ gives the total number of miles, $y$, the train traveled if the trip was $x$ hours long and $x>3$. It follows that $y=173+53(x-3)$, which is equivalent to $y=173+53x-159$, or $y=53x+14$.