Slope Calculator

Find the slope, y-intercept, and equation of a line from two points or point-slope form.

Point 1 (x₁, y₁)

x₁

y₁

Point 2 (x₂, y₂)

x₂

y₂

Example

Find the slope between points (1, 2) and (4, 8):

Slope = (8 - 2) / (4 - 1) = 6 / 3 = 2
For every 1 unit right, the line goes up 2 units
Perpendicular slope = -1/2 = -0.5
Line equation: y = 2x + 0

How to Use This Calculator

Identify two points on the line: Point 1 (x₁, y₁) and Point 2 (x₂, y₂)
Enter the coordinates of the first point in the x₁ and y₁ fields
Enter the coordinates of the second point in the x₂ and y₂ fields
Click Calculate to find the slope, angle, perpendicular slope, y-intercept, distance, and midpoint
The calculator also shows whether the line is rising, falling, horizontal, or vertical

Formula

Slope m = (y₂ - y₁) / (x₂ - x₁) = Δy / Δx (rise over run). Angle θ = arctan(m). Perpendicular slope = -1/m. Line equation: y = mx + b where b = y₁ - mx₁

Frequently Asked Questions

What does slope represent?▼

Slope measures the steepness and direction of a line. It's the ratio of vertical change (rise) to horizontal change (run). Positive slope means the line rises from left to right, negative means it falls.

What is an undefined slope?▼

An undefined slope occurs when the line is vertical (x₂ = x₁). Division by zero is undefined, so we say the slope is undefined. The line equation is x = constant.

How do I find the perpendicular slope?▼

Perpendicular lines have slopes that are negative reciprocals. If one line has slope m, the perpendicular line has slope -1/m. For example, if m = 2, the perpendicular slope is -1/2.

What is the y-intercept?▼

The y-intercept (b) is where the line crosses the y-axis (when x = 0). Using point-slope form with the calculated slope and one point: b = y - mx.