SAT Math · Heart of Algebra
Linear functions and their graphs
Slope, intercepts, and reading linear graphs in context.
What's tested in this subtopic
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.
Tactics that actually move your score
Always identify what slope represents in the units of the problem before answering. If the question asks "what does the slope mean," restate it in plain English with units: "the cost increases by $0.15 for each additional minute." If the answer choices look numerical when the question is interpretive, you've probably misread the question. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy A bicycle rental company charges a flat fee of $27 plus $8 per hour. If C(h) represents the total cost in dollars for h hours, which of the following best repr…
- Easy What is the slope of the line passing through (0, 1) and (-4, 1)?
- Medium A bicycle rental company charges a flat fee of $29 plus $4 per hour. If C(h) represents the total cost in dollars for h hours, which of the following best repr…
- Medium What is the slope of the line passing through (-1, -3) and (-2, -4)?
- Medium A bicycle rental company charges a flat fee of $66 plus $5 per hour. If C(h) represents the total cost in dollars for h hours, which of the following best repr…
- Hard What is the slope of the line passing through (2, -3) and (-3, -1)?
- Easy A bicycle rental company charges a flat fee of $64 plus $8 per hour. If C(h) represents the total cost in dollars for h hours, which of the following best repr…
- Easy What is the slope of the line passing through (1, 3) and (0, 4)?
- Medium 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 repr…
- Medium What is the slope of the line passing through (-5, -2) and (3, -3)?
- Medium 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 repr…
- Hard What is the slope of the line passing through (-3, 1) and (5, -2)?
- Easy 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 repr…
- Easy What is the slope of the line passing through (-4, -1) and (-3, -1)?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in SAT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.