One Line | Two Lines | Line through Two Points

Calculate Line through Two Points

Calculator for the linear equation from the coordinates of two given points. Two points can always be connected by a straight line, which is exactly defined by these points. The linear equation y = mx + b can be calculated from the x- and y-coordinates of both points with m = (y₂-y₁) / (x₂-x₁) and b = y₁ - mx₁. Please enter the coordinates of the two points, the linear equation will be calculated.

First point: x₁ = , y₁ =

Second point: x₂ = , y₂ =

Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.



Linear equation:

Example: a line through the points (1|5) and (3|2) has the linear equation y = -1.5x + 6.5.

Exactly one straight line always passes through two points that are not at the same location. A straight line is precisely defined by two different points that lie on it. From such two different points on a straight line, the linear equation can be determined using the formula above. The linear equation is a functional equation by which the straight line can be represented in a coordinate system. For each input value x, a function value y is calculated using the linear equation. If you enter 10 for x in the linear equation in the example, you get the value y as -8.5. The point (10|-8.5) therefore also lies on this line. In this way, you can calculate the y-value for each x-value of the line and theoretically find all points on the line, although there are, of course, infinitely many of these. This applies to all straight lines except those that are perpendicular. Perpendicular lines are described by constant y-values, for example, y=1. There is no value x here, so this is not a functional equation.
There term linear equation implies that there are also nonlinear equations. For example, if x² appears instead of x, then it is a quadratic equation. If you plot points on lines or other functions in a coordinate system, you get function graphs. See the function graph plotter for more information.

Last updated on 07/01/2025. Author: Jürgen Kummer

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