Rise Over Run

Pre-Algebra · Axiom Academy

The slope of a line is one number — how far it rises for every step you run across. Walk up a line like a staircase. Each time you take a step you go across by some amount — the run — and up by some amount — the rise . The slope is just the rise divided by the run, and it stays the same the whole way up the line. run = horizontal change (how far across) rise = vertical change (how far up) You usually do not get a staircase drawn for you — you get two points. The run is the change in x , and the rise is the change in y . Subtract the coordinates and divide. The Greek letter Δ (delta) means "change in," so is the rise and is the run. Worked from the figure: the points (1, 2) and (4, 5) Run: x goes from 1 to 4, so (right 3). Rise: y goes from 2 to 5, so (up 3). 3. When the Line Falls: Negative Slope Nothing changes when a line goes down from left to right — you still take rise over run. The only difference is that the rise is negative , because you step down instead of up, and that makes the whole slope negative. Worked from the figure: the points (1, 5) and (4, 2) Rise: y goes from 5 to 2, so (down 3). Line climbs left to right — rise and run share a sign, so . Line falls left to right — rise is negative while run is positive, so . Slope is rise over run — one number that measures how steep a line is, and which direction it tilts. Scroll up to revisit any step.

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