Two Variables, One Line
Slope as rise over run
Measure how steep a line is.
The slope (gradient) of a line is its steepness, like the steepness of a hill or a ramp.
- going up from left to right: positive slope;
- going down: negative slope.
Slope = rise ÷ run = (y2 – y1)/(x2 – x1). Through A(2, 0) and B(4, 3): rise 3, run 2, slope 3/2.
The order of the points does not matter, as long as you keep it the same top and bottom: (2 – 5)/(–1 – (–4)) = –1, and (5 – 2)/(–4 – (–1)) = –1.
Any two points on the line give the same slope. B(4, 3) to D(8, 9) gives 6/4 = 3/2 again.
A slope tells you how to walk along the line. Slope 3/2 means: 2 to the right, 3 up. So from A(2, 0), going 6 to the right (and 9 up) lands at (8, 9).
Ramps. A slope of 1/12 means 12 cm of run for each 1 cm of rise, so a height of 18 cm needs 216 cm of run.
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