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).
Understanding slope — rise over run
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.
A common mistake, and the fix
Putting the run on top.
Between (0, 0) and (2, 4) the line rises 4 and runs 2, so the slope is 4/2 = 2; writing run over rise gives 2/4 = 1/2, a much less steep line. Keep the order: rise, then run, the change in y over the change in x.
Try a few
Through (0, 0) and (3, 6) — slope?
rise 6, run 3.
Through (1, 1) and (4, 2) — slope?
rise 1, run 3.
Through (0, 0) and (5, 10) — slope?
rise 10, run 5.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
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