Math Tools
Slope Calculator
Calculate slope, rise, run, and the equation of a line from two points.
Slope Calculator
Find the slope between two points, along with the rise, run, and line equation.
Slope formula
m = (y₂ - y₁) / (x₂ - x₁)
Results
Slope
2
Rise
6
Run
3
Line equation
y = 2x
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What this slope calculator does
This calculator finds the slope between two points, shows the rise and run, and gives the line equation in slope-intercept form when the line is not vertical.
What is a slope calculator?
A slope calculator is a math tool that finds the steepness and direction of a line from two points on a graph. It helps you calculate slope, rise, run, and the equation of the line without doing the algebra manually.
This is useful in algebra, geometry, coordinate graphing, physics, engineering, and any situation where you need to understand how one value changes compared with another.
How to find slope from two points
To find slope from two points, subtract the first y-value from the second y-value to get the rise. Then subtract the first x-value from the second x-value to get the run. Finally, divide rise by run.
The slope formula is:m = (y₂ - y₁) / (x₂ - x₁)
If the run is zero, the line is vertical and the slope is undefined. If the rise is zero, the line is horizontal and the slope is zero.
Slope formula, rise, and run explained
Slope
Slope measures the steepness and direction of a line.
Rise
Rise is the vertical change between two points, or y₂ - y₁.
Run
Run is the horizontal change between two points, or x₂ - x₁.
Slope calculation examples
These examples show how to calculate slope, rise, run, and line equations from two points.
| Points | Rise | Run | Slope | Equation |
|---|---|---|---|---|
| (1, 2) and (4, 8) | 6 | 3 | 2 | y = 2x |
| (2, 5) and (6, 9) | 4 | 4 | 1 | y = x + 3 |
| (-1, 3) and (3, 1) | -2 | 4 | -0.5 | y = -0.5x + 2.5 |
| (0, 4) and (5, 4) | 0 | 5 | 0 | y = 4 |
Slope reference table
| Slope type | Meaning | Example |
|---|---|---|
| Positive slope | Line rises from left to right | m = 2 |
| Negative slope | Line falls from left to right | m = -3 |
| Zero slope | Horizontal line | m = 0 |
| Undefined slope | Vertical line | run = 0 |
How to calculate the equation of a line from slope
Once you know the slope and one point on the line, you can write the equation of the line. A common form is slope-intercept form:y = mx + b
In this form, m is the slope and b is the y-intercept. The calculator uses the slope and one of the points to determine the line equation automatically when the line is not vertical.
When a slope calculator is useful
A slope calculator is useful for algebra homework, graphing lines, coordinate geometry, physics problems, data trend analysis, and engineering calculations. It is especially helpful when checking answers or working quickly with multiple point pairs.
Students often use it to understand linear equations, while professionals may use slope concepts to measure gradients, inclines, rates of change, and directional movement.
Slope calculator FAQ and common slope questions
How do you calculate slope from two points?
Subtract the first y-value from the second y-value, subtract the first x-value from the second x-value, and divide rise by run. This gives m = (y₂ - y₁) / (x₂ - x₁).
What does a positive slope mean?
A positive slope means the line rises from left to right. As x increases, y also increases.
What does a negative slope mean?
A negative slope means the line falls from left to right. As x increases, y decreases.
What is an undefined slope?
An undefined slope happens when the run is zero. This means the line is vertical and division by zero is not possible.
What is the difference between rise and run?
Rise is the vertical change between two points, while run is the horizontal change. Slope is the ratio of rise to run.
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