Slope — Rise over Run (Grades 7–8)
Slope measures how steep a line is: how much it rises (vertical change) for each unit it runs (horizontal change). Between two points, slope = rise/run = (change in y)/(change in x). From (0, 0) to (2, 4), the line rises 4 while running 2, so slope = 4/2 = 2 — it goes up 2 for every 1 across.
Understanding slope — rise over run
Slope measures how steep a line is: how much it rises (vertical change) for each unit it runs (horizontal change). Between two points, slope = rise/run = (change in y)/(change in x). From (0, 0) to (2, 4), the line rises 4 while running 2, so slope = 4/2 = 2 — it goes up 2 for every 1 across.
Key Idea
Slope measures how steep a line is: how much it rises (vertical change) for each unit it runs (horizontal change). Between two points, slope = rise/run = (change in y)/(change in x). From (0, 0) to (2, 4), the line rises 4 while running 2, so slope = 4/2 = 2 — it goes up 2 for every 1 across.
Seeing it in action
Worked example
Slope of the line through (0, 0) and (2, 4)?
Rise = 4 − 0 = 4. Run = 2 − 0 = 2. Slope = 4/2 = 2.
Rise 4, run 2, so slope is 2.
Try a few
Through (0, 0) and (3, 6) — slope?
Through (1, 1) and (4, 2) — slope?
rise 1, run 3.
Through (0, 0) and (5, 10) — slope?
Ready for the interactive lab?
Practice slope — rise over run in Numeris with instant feedback.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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