Slope Calculator – Find the Slope from Two Points
Enter two points to get the slope, the equation of the line, both intercepts, the angle, the distance and the midpoint — with every step shown and a graph.
The slope is m = (y₂ − y₁) ÷ (x₂ − x₁), or “rise over run”. For the points (1, 2) and (4, 8): m = (8 − 2) ÷ (4 − 1) = 6 ÷ 3 = 2, and the line is y = 2x + 0.
How to use Slope Calculator
- Enter the coordinates of the first point (x₁, y₁).
- Enter the coordinates of the second point (x₂, y₂). Decimals and negative numbers are fine.
- Read the slope, shown as a fraction when possible, and the equation of the line.
- Check the step-by-step working and the graph to understand the result.
The slope formula
The slope tells you how steep a line is and in which direction it goes. It is the change in y divided by the change in x between two points:
m = (y₂ − y₁) ÷ (x₂ − x₁)
People also call it “rise over run”: how far the line goes up (rise) for every step to the right (run).
What the slope tells you
| Slope | Line | Example |
|---|---|---|
| Positive | Rises from left to right | m = 2 |
| Negative | Falls from left to right | m = −1/2 |
| Zero | Horizontal | y = 3 |
| Undefined | Vertical | x = 4 |
A vertical line has no slope, because the run is zero and you cannot divide by zero. The calculator tells you when that happens and gives the equation x = … instead.
Equations of a line
Once you know the slope, you can write the line in two common forms:
- Slope-intercept form: y = mx + b, where b is the y-intercept (where the line crosses the y-axis). Find b with b = y₁ − m × x₁.
- Point-slope form: y − y₁ = m(x − x₁). This is handy when you know one point and the slope.
The x-intercept, where the line crosses the x-axis, is −b ÷ m.
Angle, distance and midpoint
The angle of the line with the x-axis is arctan(m); a slope of 1 is 45°. The distance between the points uses Pythagoras: √((x₂ − x₁)² + (y₂ − y₁)²). The midpoint is the average of the x values and of the y values.
Slope in real life
Slope is used for roads and ramps (as a percentage: slope × 100), roofs (rise per 12 inches of run), and in graphs of speed or cost per unit. A road with a 6% grade rises 6 m for every 100 m. For other homework, the LCM & GCF Calculator shows its working too.
You may also find these free tools useful: GPA Calculator, LCM & GCF Calculator and Standard Deviation Calculator.
Frequently asked questions
How do you find the slope from two points?
Subtract the y values, subtract the x values in the same order, and divide: m = (y₂ − y₁) ÷ (x₂ − x₁).
What is the slope of a horizontal line?
Zero. The y value never changes, so the rise is 0.
What is the slope of a vertical line?
It is undefined, because the run (x₂ − x₁) is 0 and you cannot divide by zero. The equation is x = a constant.
How do I write the equation of a line from two points?
Find the slope m, then b = y₁ − m × x₁. The equation is y = mx + b. The calculator shows both steps.
How do I turn a slope into a percentage or angle?
Multiply the slope by 100 for a percentage grade. For the angle, use arctan(slope); for example, a slope of 0.5 is about 26.6°.
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