Slope of a Line
Steepness of a straight line.
Formula
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Example
Through (1, 2) and (4, 11): m = (11−2)/(4−1) = 9/3 = 3.
How it works
The slope of a line tells you how much the vertical value changes for each 1 unit you move horizontally. It is found by taking the change in y, called "rise," and dividing it by the change in x, called "run." This works because a straight line has a constant rate of change between any two points on it.
When to use it
Use this formula whenever you need to find how steep a straight line is from two points on a graph or in coordinate geometry. It is also useful for checking whether lines are parallel, perpendicular, or increasing/decreasing.
Worked example, step by step
Find the slope through (-3, 5) and (2, -5). Use m = (y_2 - y_1) / (x_2 - x_1) Substitute: m = (-5 - 5) / (2 - (-3)) Simplify: m = -10 / 5 Final answer: m = -2
Common mistakes to avoid
- Subtracting x-values from y-values in the wrong order
- Forgetting that subtracting a negative number becomes addition
- Reversing the points inconsistently, which can change the sign if done unevenly
Did You Know?
Slope — "rise over run" — is the everyday ancestor of the derivative in calculus.
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