Algebra
Slope of a line
Slope measures how steeply a line rises or falls: the change in y divided by the change in x between any two points on the line, m = (y₂ − y₁)/(x₂ − x₁).
Why it matters
Slope is the first idea of rate of change, and it becomes the derivative in calculus. Students who understand slope as 'per one unit of x' read graphs, tables and word problems far more reliably.
Worked example
Find the slope of the line through (−2, 5) and (4, −7)
- 1Label the points. (x₁, y₁) = (−2, 5) and (x₂, y₂) = (4, −7)
- 2Apply the formula. m = (−7 − 5) / (4 − (−2))
- 3Simplify carefully. m = −12 / 6
Answer: m = −2 (the line falls 2 units for every 1 unit right)
Common mistakes
- Subtracting the coordinates in a different order on the top and the bottom.
- Writing run over rise instead of rise over run.
- Reading a negative slope as positive because the graph was scanned left to right without checking direction.
How to check your answer
- Sketch the two points: a falling line must give a negative slope.
- State the slope in words — 'y drops 2 for every 1 increase in x' — to confirm it matches the picture.
Related topics
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