Slope Calculator
Find the slope between two points, with the line equation, angle, distance and midpoint.
Results
| Item | Value |
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Steps
| Step | Working |
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Quick Answer
Slope is rise over run: m = (y₂ − y₁) ÷ (x₂ − x₁). Between the points (1, 2) and (4, 8), the rise is 6 and the run is 3, so the slope is 2. The line equation is y = 2x + 0.
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Table of Contents
How This Slope Calculator Works
Slope measures how steep a line is. Enter two points, and the calculator finds the slope, the line equation in y = mx + b form, the angle, the distance between the points, and the midpoint.
Quick explanation: m = rise ÷ run.
- Positive slope: the line rises from left to right.
- Negative slope: the line falls from left to right.
- Zero: a flat line. A vertical line has an undefined slope.
Core Formulas
- Slope: m = (y₂ − y₁) ÷ (x₂ − x₁)
- Y-intercept: b = y₁ − m × x₁
- Angle: arctan(m)
- Distance: √((x₂ − x₁)² + (y₂ − y₁)²)
- Midpoint: ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
Worked Example
Find the slope between (0, 0) and (2, −1).
- Rise = −1 − 0 = −1
- Run = 2 − 0 = 2
- Slope = −1 ÷ 2 = −0.5
- Equation: y = −0.5x + 0
Common Mistakes
- Mixing the order: subtract x and y in the same point order.
- Dropping a negative: take care when subtracting a negative number.
- Dividing by zero: if both x values match, the line is vertical.
Frequently Asked Questions
Subtract the y values, subtract the x values in the same order, then divide: m = (y₂ − y₁) ÷ (x₂ − x₁).
It means the line is flat, because y does not change.
It is the slope of a vertical line. The run is 0, and you cannot divide by 0.
It is the slope-intercept form of a line. m is the slope, and b is where the line crosses the y-axis.
Take the arctangent of the slope. A slope of 1 is an angle of 45°.
References & Sources
| Source | Used For | Link |
|---|---|---|
| Wikipedia, Slope | Definition and formula for slope. | https://en.wikipedia.org/wiki/Slope |
| Wikipedia, Linear equation | Slope-intercept form. | https://en.wikipedia.org/wiki/Linear_equation |