Coordinate Graphs, Lines & Slope
rise over run
“Rise over run” is the everyday phrase for computing slope: how much you go up (the rise) divided by how much you go across (the run) as you travel between two points on a line.
“Rise” is the vertical change, y₂ − y₁; “run” is the horizontal change, x₂ − x₁. Slope is rise ÷ run. A staircase makes this vivid: if each step rises 7 inches and runs 11 inches deep, the staircase’s slope is 7/11.
Watch the signs. Going from left to right, a downhill line has a negative rise (you go down), so its slope comes out negative. And if the run is 0 — a vertical line — “rise over run” has no value, because you cannot divide by zero.
From (0, 1) to (5, 4): rise = 4 − 1 = 3, run = 5 − 0 = 5, so slope = 3/5.
Up 3, across 5: slope 3/5.
Also called
See also