SAT · Heart of Algebra · Linear functions and their graphs
Question sat-q-00025
Medium Multiple choice Calculator OK
The question
A bicycle rental company charges a flat fee of $57 plus $5 per hour. If C(h) represents the total cost in dollars for h hours, which of the following best represents C(h)?
- C(h) = 5h + 57
- C(h) = (57 + 5)h
- C(h) = 57h + 5
- C(h) = 57 − 5h
Show answer & worked solution
Answer: C(h) = 5h + 57
Worked solution. The flat fee $57 does not depend on h, so it is the y-intercept. The hourly rate $5 multiplies h. Therefore C(h) = 5h + 57.
Why each wrong choice is wrong. Swapping the slope and intercept is the most common error here. The trap distractor multiplies the flat fee by h instead of treating it as a constant.
Test-day tactic. When you see 'flat fee plus per-X charge', the flat fee is always the y-intercept and the per-X charge is the slope.
About this question type
Items here ask you to interpret slope and y-intercept in real-world contexts (revenue per item, cost per minute), to write the equation of a line from two points or from a description, or to identify which graph corresponds to a given equation. The hardest items combine all three at once.
You will see a question shaped like this one on roughly every other official SAT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.