Slope measures how steep a line is and in which direction it tilts. You find it by comparing the vertical change to the horizontal change between two points on the line, often summed up as rise over run.
Step by step
- Pick two points on the lineChoose two clear points and write their coordinates, for example (1, 2) and (4, 8), labeling them as point one and point two.
- Find the riseSubtract the first y value from the second y value. Here 8 minus 2 gives a rise of 6.
- Find the runSubtract the first x value from the second x value in the same order. Here 4 minus 1 gives a run of 3.
- Divide rise by runDivide the rise by the run to get the slope. In the example, 6 divided by 3 gives a slope of 2.
- Interpret the resultA positive slope rises left to right, a negative slope falls, zero is a flat horizontal line, and a vertical line has an undefined slope.
Handy tips
- Keep the points in the same order for both the top and bottom of the fraction, or the sign will be wrong.
- Reduce the slope fraction to lowest terms for a cleaner answer.
- In the equation y = mx + b, the number m is the slope.
FAQ
What is the slope formula?
Slope equals the change in y divided by the change in x, written as (y2 minus y1) divided by (x2 minus x1).
What does a negative slope mean?
It means the line goes downhill from left to right. As x increases, y decreases.
Why is a vertical line's slope undefined?
A vertical line has no horizontal change, so the run is zero. Dividing by zero is undefined, so the slope does not exist.