ACT · Coordinate Geometry · Lines, slopes, and intercepts
Question act-q-00403
Medium Multiple choice No calculator
The question
What is the slope of the line passing through (0, 5) and (4, -2)?
- -1.25
- 1.75
- 0.57
- -1.75
Show answer & worked solution
Answer: -1.75
Worked solution. Slope = (y₂ − y₁) / (x₂ − x₁) = (-2 − 5) / (4 − 0) = -7 / 4 = -1.75.
Why each wrong choice is wrong. Reversing the subtraction order in the numerator without doing the same in the denominator gives the negative of the slope — a common slip.
Test-day tactic. Pick which point is (x₁, y₁) and which is (x₂, y₂) before computing, and stick with the choice. The order doesn't matter as long as it's consistent.
About this question type
Items test the slope formula, the slope-intercept and point-slope forms, and the slope rules for parallel (equal) and perpendicular (negative reciprocal) lines.
You will see a question shaped like this one on roughly every other official ACT 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.