Slope Calculator
Slope Calculator
Enter the coordinates of two points (x₁, y₁) and (x₂, y₂). This calculates the slope of the line through them, the y-intercept, and the full slope-intercept equation (y = mx + b).
Slope is the change in y divided by the change in x between the two points — often described as "rise over run" — and its sign tells you the line's direction at a glance: positive rises left to right, negative falls left to right, and exactly zero is a perfectly horizontal line. A vertical line is the one case slope can't describe, since the change in x would be zero and division by zero is undefined — this calculator flags that case explicitly rather than returning a misleading result.
- Formula: slope (m) = (y₂ − y₁) ÷ (x₂ − x₁) — the change in y divided by the change in x, often called "rise over run."
- What the sign means: a positive slope rises left to right, a negative slope falls left to right, and a slope of zero is a perfectly horizontal line.
- Vertical lines have undefined slope: when both points share the same x-coordinate, the line is vertical and the slope formula divides by zero — this calculator flags that case rather than showing an error.
What does a slope of 3 actually mean?
It means for every 1 unit you move right (increase x by 1), the line rises 3 units (y increases by 3) — the larger the absolute value of the slope, the steeper the line.
How is the y-intercept calculated from the slope?
Once you know the slope, plug one of the original points and the slope into y = mx + b and solve for b — that's exactly what this calculator does automatically.
Slope Calculator
Enter the coordinates of two points (x₁, y₁) and (x₂, y₂). This calculates the slope of the line through them, the y-intercept, and the full slope-intercept equation (y = mx + b).
Slope is the change in y divided by the change in x between the two points — often described as "rise over run" — and its sign tells you the line's direction at a glance: positive rises left to right, negative falls left to right, and exactly zero is a perfectly horizontal line. A vertical line is the one case slope can't describe, since the change in x would be zero and division by zero is undefined — this calculator flags that case explicitly rather than returning a misleading result.
- Formula: slope (m) = (y₂ − y₁) ÷ (x₂ − x₁) — the change in y divided by the change in x, often called "rise over run."
- What the sign means: a positive slope rises left to right, a negative slope falls left to right, and a slope of zero is a perfectly horizontal line.
- Vertical lines have undefined slope: when both points share the same x-coordinate, the line is vertical and the slope formula divides by zero — this calculator flags that case rather than showing an error.
What does a slope of 3 actually mean?
It means for every 1 unit you move right (increase x by 1), the line rises 3 units (y increases by 3) — the larger the absolute value of the slope, the steeper the line.
How is the y-intercept calculated from the slope?
Once you know the slope, plug one of the original points and the slope into y = mx + b and solve for b — that's exactly what this calculator does automatically.