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Y-Intercept (Mathematics Glossary)

What Is the Y-Intercept?

The y-intercept of a line is the y-coordinate of the point where a line, curve or surface crosses the y-axis.

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

What Is the Y-Intercept of a Line?

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

The line below crosses the y-axis at y = 3. The y-intercept of the line is 3.

The y-intercept is 3

Read more about finding the y-intercept of a line

The Y-Axis Crosses the X-Axis When X = 0

The y-axis crosses the x-axis when x = 0.

This means that all points on the y-axis have x = 0.

This is useful, because it let's us find the y-intercept of a line or a curve when we know its equation.

  • Finding the Y-Intercept of a Line from a Linear Equation

    The y-intercept of a line can be found from the equation of a line (called a linear equation).

    The slope-intercept form of a linear equation is:

    y equals m x plus c

    In this equation, y and x are variables. m and c are letters that stand in for numbers. An example of a linear equation would be y = 2x + 1 (the m = 2 and c = 1).

    The y-intercept occurs when the line crosses the y-axis. On the y-axis, x = 0.

    The y-intercept of this equation is c.

  • Finding the Y-Intercept of a Line from a Function

    The linear equation is an example of a function. For any value of x, it tells you y.

    We can find the y-intercept of any function by substituting x = 0.

    Read more about finding the y-intercept of a function

More About the Y-Intercept

The slider below gives more information about the y-intercept:

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Here's a second test on the y-intercept.
Here's a third test on the y-intercept.

Note

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