Slope Calculator

Step 1: Enter the x and y coordinates of Point 1 (x₁, y₁).

Step 2: Enter the x and y coordinates of Point 2 (x₂, y₂).

Step 3: Click Calculate to get the slope, y-intercept, equation, angle, distance, and midpoint.

Slope measures how steep a line is — specifically, how much the line rises for each unit it runs to the right. A slope of 2 means the line goes up 2 units for every 1 unit to the right. A slope of zero means the line is horizontal, and an undefined slope means the line is vertical.

Positive slopes go up from left to right; negative slopes go down. The larger the absolute value, the steeper the line.

Slope is a foundational concept in algebra, calculus (where it becomes the derivative), and physics (velocity is the slope of a position-time graph).

m = (y₂ − y₁) / (x₂ − x₁)

The numerator is the 'rise' (change in y); the denominator is the 'run' (change in x).

Line equation (slope-intercept form): y = mx + b, where b = y₁ − m·x₁

Example: Points (1, 2) and (4, 8)
Rise = 8 − 2 = 6
Run = 4 − 1 = 3
Slope m = 6 ÷ 3 = 2
b = 2 − 2·1 = 0 → y = 2x

Example 1: Points (1, 2) and (4, 8) → slope 2, equation y = 2x.

Example 2: Points (0, 5) and (2, 1) → slope −2, equation y = −2x + 5 (line falling).

Example 3: Points (3, 4) and (3, 9) → undefined slope (vertical line x = 3).

Order matters consistently — subtract Point 1 from Point 2 in both numerator and denominator.

Vertical line = undefined slope — the calculator flags this.

Parallel lines have the same slope.

Perpendicular lines have slopes that multiply to −1.