Slope Calculator

Slope (m) measures the steepness and direction of a line. It is calculated as the rise divided by the run: m = (y2 − y1) / (x2 − x1). A positive slope means the line goes upward from left to right, while a negative slope means it goes downward.

A slope of zero means the line is perfectly horizontal — y does not change as x changes. An undefined slope occurs when the two x-values are equal (vertical line), which would cause division by zero in the formula.

If you know one point (x1, y1) and the slope m, you can use the point-slope form: y − y1 = m(x − x1). Rearranging gives you the full line equation and lets you find any other point on the line.

The y-intercept is the point where the line crosses the y-axis (when x = 0). Once you have the slope m and one coordinate point, use b = y1 − m × x1 to calculate it. The full line is then expressed as y = mx + b.

The x-intercept is the point where the line crosses the x-axis (when y = 0). Solving 0 = mx + b gives x = −b / m. This is undefined if the slope is zero (horizontal line never crosses the x-axis unless it lies on it).

The angle of inclination θ is the angle the line makes with the positive x-axis. It is calculated as θ = arctan(m), where m is the slope. A steeper line has a larger angle, approaching 90° for near-vertical lines.

Parallel lines have equal slopes (m1 = m2). Perpendicular lines have slopes that are negative reciprocals of each other, meaning m1 × m2 = −1. For example, if one line has a slope of 2, a perpendicular line has a slope of −0.5.

Yes. You can enter any real number for the coordinates, including negative values and decimals. The calculator will correctly compute the slope, intercepts, and angle regardless of the sign or magnitude of the inputs.