Calculating Slope

Algebra 1 · Axiom Academy

Finding the slope of a line from two points using rise over run. Find the slope of the line passing through the points (3, 5) and (-1, -3) . Going from P_1(3, 5) down to P_2(-1, -3) : the line falls 8 (the rise, in red) and moves 4 to the left (the run, in green). Slope is rise over run. Nice work — you found the slope through two points by reducing it to rise over run. Pick your two points: label them (x_1, y_1) and (x_2, y_2) . Which one you call 1 vs 2 is your choice — just stay consistent. Rise = y_2 - y_1 : here -3 - 5 = -8 , so the line drops 8 units. Run = x_2 - x_1 : here -1 - 3 = -4 . Subtract in the same order you used for the rise. Slope . A negative over a negative gives a positive slope. A positive slope means the line goes up as you move from left to right — for every 1 unit right, it rises 2.

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