ACT Math · Coordinate Geometry
Lines, slopes, and intercepts
Slope, point-slope form, and parallel/perpendicular lines.
What's tested in this subtopic
Items test the slope formula, the slope-intercept and point-slope forms, and the slope rules for parallel (equal) and perpendicular (negative reciprocal) lines.
Tactics that actually move your score
Two lines are parallel iff they have equal slopes; perpendicular iff their slopes multiply to −1. 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 What is the slope of the line passing through (5, 3) and (-3, -4)?
- Easy What is the slope of the line passing through (-1, 5) and (-5, 0)?
- Medium What is the slope of the line passing through (4, 0) and (5, 1)?
- Medium What is the slope of the line passing through (0, 0) and (-4, -1)?
- Medium What is the slope of the line passing through (-1, 3) and (-4, 3)?
- Hard What is the slope of the line passing through (5, 4) and (2, -4)?
- Easy What is the slope of the line passing through (4, 0) and (-4, -3)?
- Easy What is the slope of the line passing through (-2, -1) and (-5, -4)?
- Medium What is the slope of the line passing through (-3, 3) and (-5, -5)?
- Medium What is the slope of the line passing through (4, -4) and (5, -3)?
- Medium What is the slope of the line passing through (0, 5) and (4, -2)?
- Hard What is the slope of the line passing through (5, -1) and (4, 4)?
- Easy What is the slope of the line passing through (-4, 0) and (1, -5)?
- Easy What is the slope of the line passing through (0, 4) and (-4, 3)?
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 ACT 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.