Slope Calculator

Enter two points. You get the slope, midpoint, distance, and the line equation.

Smart Tips

• Slope is rise over run: (y₂ − y₁) / (x₂ − x₁).

• If the x-coordinates match and the y-coordinates do not, the line is vertical and the slope is undefined.

• The same point twice does not determine a line. Enter two different points.

• Distance is the straight-line distance formula, not a road distance.

The Formula

m = (y₂ − y₁) / (x₂ − x₁)

m = Slope
Rise divided by run

M = Midpoint
((x₁ + x₂) / 2, (y₁ + y₂) / 2)

d = Distance
√((x₂ − x₁)² + (y₂ − y₁)²)

b = Intercept
From y = mx + b, when m exists

A vertical line is written x = constant. The page does not divide by zero in that case. A horizontal line has slope 0 and equation y = constant. Fractions in the equation are reduced.

Key Insights

Vertical lines

A run of 0 would mean dividing by zero. The slope is reported as undefined and the equation is x = the shared x-coordinate.

Two points, one line

Two different points determine one line. The midpoint and the distance are reported with the slope.

Not a route

The distance is the straight segment between the points. It is not driving distance and it does not follow roads.

Reduced slope

When the coordinates are whole numbers or decimals, the slope is a reduced fraction, such as 4/3, and the equation uses that fraction.

Frequently Asked Questions

The slope, the midpoint, the straight-line distance, and the equation of the line through the two points. The steps show the rise, the run, and the intercept.

If both points have the same x-coordinate and different y-coordinates, the run is 0. The slope is undefined. The equation is x = that x-coordinate. The page does not divide by zero.

One point does not determine a line. The page rejects that pair. Move one of the points.

No. Distance is √((x₂ − x₁)² + (y₂ − y₁)²), the length of the straight segment. From (0, 0) to (3, 4) that length is 5.

When the slope exists, the line is y = mx + b, with m and b reduced. A slope of 4/3 through the origin is y = (4/3)x. A vertical line is x = constant.

Slope, including an undefined slope for a vertical line, follows OpenStax Elementary Algebra 2e, section 4.4. The distance and the midpoint follow OpenStax Intermediate Algebra 2e, section 11.1. The line is y = mx + b when the slope exists. No outside data feed is used.

Responsive Ad Space

Slope

Enter values to calculate

Midpoint

Distance

Equation

Note:Distance is the straight-line distance between the two points, not a driving distance. A vertical line has an undefined slope, and the page does not divide by zero.