What is slope?
Slope tells how steep a straight line is. It compares vertical change to horizontal change, so learners can describe whether a line rises, falls, stays flat, or becomes vertical.
Genius Littles
Interactive math tool
Calculate Slope with the Interactive Slope Explorer
Use this interactive slope calculator to calculate slope from two points, rise and run, or different forms of a line equation. Move the points on the graph to see how slope controls the direction and steepness of a line.
Explore rise over run
Drag point A or B to see how rise, run, and slope change.
How do you calculate slope?
To calculate slope, divide rise by run. With two points, use m = (y2 - y1) / (x2 - x1).
Calculate slope from two points
Subtract the y-values to find the rise. Subtract the x-values in the same order to find the run. Then simplify the fraction.
Calculate slope using rise over run
Rise over run means vertical movement divided by horizontal movement. If the run is zero, the slope is undefined because division by zero is not allowed.
Find slope from a line equation
In y = mx + b, the coefficient of x is the slope. In standard form Ax + By = C, the slope is -A/B when B is not zero.
Positive and negative slopes
A positive slope rises from left to right. A negative slope falls from left to right. The sign tells the direction while the size tells the steepness.
Zero and undefined slopes
A horizontal line has slope 0 because its rise is zero. A vertical line has undefined slope because its run is zero.
Slope in y=mx+b
The number m controls the line's steepness and direction. The number b marks where the line crosses the y-axis.
Real-life examples of slope
Road gradients, wheelchair ramps, roofs, hills, staircases, temperature graphs, and distance-time graphs all use slope to describe change.
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Frequently asked questions
How do you calculate slope?
Divide rise by run. Rise is the change in y, and run is the change in x.
What is the slope formula?
The slope formula is m = (y2 - y1) / (x2 - x1).
How do you calculate slope from two points?
Find y2 - y1, find x2 - x1, then divide and simplify.
How do you calculate slope from rise and run?
Use m = rise / run. For example, a rise of 6 and run of 3 gives m = 2.
How do you find slope from y=mx+b?
The slope is the coefficient of x. In y = 3x - 4, the slope is 3.
How do you find slope from standard form?
For Ax + By = C, use m = -A/B as long as B is not zero.
What does a negative slope mean?
A negative slope means the line falls from left to right.
What is the slope of a horizontal line?
The slope of a horizontal line is 0.
Why is the slope of a vertical line undefined?
A vertical line has run 0. Since division by zero is undefined, its slope is undefined.