How to Find the Y-Intercept from a Linear Equation

Finding the Y-Intercept from a Linear Equation

The y-intercept is where a line crosses the y-axis.

The y-intercept is where the line crosses the y-axis

A line can be represented by a linear equation. We can find the y-intercept from a linear equation.

Interactive Widget

You can use this interactive widget to create a graph of your linear equation and to see the y-Intercept. Use the buttons to change the values of the linear equation.

Change the Linear Equation
y+ y-
x+ x-
y-intercept + y-intercept -

Oops, it's broken!

Turn your phone on its side to use this widget.

Real Examples of Finding the Y-Intercept from a Linear Equation

Finding the y-intercept of a line from a linear equation is easy.

Here are some linear equations, which represent lines. We show how to find the y-intercept from the linear equation.

  • The y-intercept of y = 2x + 1 is 1.

    y-intercept of y equals 2 x plus 1 is 1

    Look at the constant term (the one that does not contain the variables x or y). This is the y-intercept.

  • The y-intercept of y = −3x + 3 is 3.

    y-intercept of y equals minus 3 x plus 3 is 3
  • The y-intercept of y = x − 2 is −2.

    y-intercept of y equals x minus 2 is minus 2

    Look at the sign in front of the constant. If it is a minus sign (−) the y-intercept must also have a minus sign. The y-intercept is negative; it is below the x-axis.

  • The y-intercept of y = 4x is 0.

    y-intercept of y equals  4 x is 0

    There is no constant term. The y-intercept is 0.

Understanding Finding the Y-Intercept from a Linear Equation

A linear equation (in slope-intercept form) is given in the form below:

y equals m x plus c

To find the y-intercept, we need to find out where the line represented by this equation crosses the y-axis.

x equals 0 at the y-axis

Along the y-axis, x has a value of 0.

This means that if we substitute x = 0 into a linear equation and find out what y equals, we will find the y-intercept.

y equals c

The y-intercept is the constant term (here represented by the letter c, but can be any number).

Slider

The slider below gives a real example of how to find the y-intercept from a linear equation.

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More Examples of Finding the Y-Intercept of a Line from Linear Equations

All of the linear equations we have seen in this lesson have been in slope-intercept form (y = mx + c).

This is the easiest form of linear equation to find the y-intercept. You must be able to find the y-intercept in all forms of linear equation.

The method is the same. Substitute x = 0 into the linear equation and solve for y. The main difference is it may need more effort to rearrange the equation to solve for y.

See Also

What is the slope of a line? What is the y-coordinate? What is the y-axis? What is a linear equation?