Finding the Y-Intercept from a Linear Equation
(KS3, Year 9)

The Lesson

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 a linear equation and see its y-intercept. Use the buttons to change the values of the linear equation.
Change the Equation
y
x
y-intercept

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).

Lesson Slides

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

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.

Positive, Zero and Negative Y-Intercepts

A positive y-intercept means the line crosses the y-axis above the x-axis:

positive y intercept A zero y-intercept means the line crosses the y-axis at the origin:

zero y-intercept A negative y-intercept means the line crosses the y-axis below the x-axis:

negative y-intercept
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See Also

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