Slope Calculator
Find the slope of the line through two points, plus its equation, angle, distance and midpoint.
Slope (m)
1.5
- As a fraction
- 3/2
- Line equation
- y = 1.5x + 0.5
- Angle with the x-axis
- 56.31°
- Distance between the points
- 7.2111
- Midpoint
- (3, 5)
The line rises 1.5 units for every 1 unit across.
Calculation breakdown
| Step | Formula | Result |
|---|---|---|
| Rise | 8 − 2 | 6 |
| Run | 5 − 1 | 4 |
| Distance | √(4² + 6²) | 7.2111 |
How it works
Enter the coordinates of two different points.
Worked example
The points (1, 2) and (5, 8):
- Rise: 8 − 2 = 6. Run: 5 − 1 = 4
- Slope: 6 ÷ 4 = 1.5, or 3/2
- Equation: b = 2 − 1.5 × 1 = 0.5, so y = 1.5x + 0.5
- Midpoint: (3, 5). Distance: √(16 + 36) = 7.2111
Sources
Frequently asked questions
How do you find the slope between two points?
Divide the change in y by the change in x, m = (y₂ − y₁) ÷ (x₂ − x₁). For the points (1, 2) and (5, 8), the rise is 6 and the run is 4, so the slope is 6 ÷ 4 = 1.5.
What does the slope mean?
It is how steep the line is. A positive slope rises to the right, a negative slope falls, and a slope of 0 is a flat line. A slope of 1 is a 45 degree angle.
What is the slope of a vertical line?
It is undefined, because the run is 0 and you cannot divide by zero. Its equation is x = a constant, and the calculator shows that.
How do I write the equation of the line?
Use y = mx + b. Find m as the slope, then b = y₁ − m × x₁. For (1, 2) and (5, 8), b = 2 − 1.5 = 0.5, so y = 1.5x + 0.5.
How do I find the angle of a line?
The angle with the x-axis is the inverse tangent of the slope. A slope of 1.5 is an angle of about 56.31 degrees.