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Equation of a Line Calculator

Select the calculation parameters and enter their values to determine the equation of a line using this equation of a line calculator.

Calculate Using the Following:

X₁:

Y₁:

X₂:

Y₂

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Our Equation of a Line Calculator helps you find the equation of any line by analyzing the vertical change divided by the horizontal change, commonly known as the "rise over run." You can also visualize the line graphically to understand its slope and intercepts.

What is the Equation of a Line?

An equation of a line represents all points lying on that line within a coordinate system. While a line has infinitely many points, only two points are required to determine its unique equation.

Equation of a line illustration

Forms of a Line Equation

There are three main ways to represent a line algebraically:

Point-Slope Form
Slope-Intercept Form
Standard Form

Point-Slope Form

This form uses one known point on the line and the slope:

y - y1 = m(x - x1)

Where:

(x1, y1) = a point on the line
m = slope of the line

It is useful for quickly writing the line equation if you know a point and slope. You can also use our Point-Slope Calculator to simplify this.

Slope-Intercept Form

The slope-intercept form expresses a line in terms of slope and y-intercept:

y = mx + c

Where:

m = slope of the line
c = y-intercept

This form is convenient for quickly plotting lines. Use the Slope-Intercept Calculator for instant results.

Standard Form

The standard form represents a line as:

Ax + By = C or Ax + By + C = 0

Where A and B are coefficients of x and y, and C is a constant. You can calculate this form using the Standard Form Calculator.

Example Equations

Point-Slope Form Example

Given point (3,5) and slope m = 6:

y - 5 = 6(x - 3)

Slope-Intercept Form Example

Given slope m = 6 and y-intercept c = 8:

y = 6x + 8

Standard Form Example

Convert y = 6x + 8 to standard form:

y = 6x + 8 → 6x - y + 8 = 0 → 6x - y = -8

Standard Form: 6x - y = -8

Finding the Y-Intercept

Set x = 0 in the line equation. Example: y = 3x - 7 → y = -7. So the y-intercept is -7.

Finding the X-Intercept

Set y = 0 in the equation. Example: y = 3x - 6 → 0 = 3x - 6 → x = 2. So the x-intercept is 2.

Slope of Parallel and Perpendicular Lines

Parallel Lines: Lines are parallel if they have equal slopes.

Perpendicular Lines: Lines are perpendicular if their slopes are negative reciprocals. For instance, a line with slope -5 has a perpendicular line slope of 1/5.

How the Equation of a Line Calculator Works

This tool allows you to compute the equation in all forms, including lines passing through two points.

Input:

Select input type: two points, one point & slope, or y-intercept & slope
Enter the corresponding values
Click calculate

Output:

Equation in point-slope, slope-intercept, and standard form
Graphical representation of the line

FAQs

How do you graph a line equation?

Use the slope (m) and y-intercept (c) from y = mx + c to plot the line.

What is the y-intercept?

The y-intercept is the point where the line crosses the y-axis. In y = mx + c, c is the y-intercept.

References

From BYU-I: Point-Slope Form of a Line. From Wikipedia: Line. From ChiliMath: How to Graph a Line.

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