Slope Calculator
Find the slope, y-intercept, and equation of a line from two points or point-slope form.
Enter Two Points
Point 1 (x₁, y₁)
Point 2 (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.