SAT · Heart of Algebra · Linear functions and their graphs
Question sat-q-00027
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The question
A bicycle rental company charges a flat fee of $43 plus $2 per hour. If C(h) represents the total cost in dollars for h hours, which of the following best represents C(h)?
- C(h) = 43h + 2
- C(h) = 2h + 43
- C(h) = (43 + 2)h
- C(h) = 43 − 2h
Show answer & worked solution
Answer: C(h) = 2h + 43
Worked solution. The flat fee $43 does not depend on h, so it is the y-intercept. The hourly rate $2 multiplies h. Therefore C(h) = 2h + 43.
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 an early position in the section, where missing them carries an outsize penalty because the curve assumes everyone in your band gets them right. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.