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Determining Intercepts

Determining Intercepts

Author: Sophia Tutorial

This lesson demonstrates how to determine intercepts.

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What's Covered

  • Finding Intercepts on a Graph
  • Finding Intercepts from a Table
  • Finding Intercepts from an Equation

Determining Intercepts

Finding Intercepts on a Graph

When we talk about a line's intercepts, we most often mean the x-intercept and the y-intercept.  These are locations where the line intercepts or crosses the x- or y- axis.  A more formal definition is as follows:

Terms to Know

  • x-intercept
  • where a line or curve intersects the x-axis, at y = 0
  • y-intercept
  • where a line or curve intersects the y-axis, at x = 0

Below is the graph of a line, with both intercepts shown:

Notice that the x-intercept always has a y-coordinate of 0, and the y-intercept always has an x-coordinate of 0. 

Determining Intercepts from a Table

Keeping the above note in mind, we can easily identify intercepts from a table of x and y values when we notice that one of the coordinates is zero!  Take a look:

We see that the second pair (0, 12) contains a zero.  In this coordinate pair, the x-coordinate is zero, which means this represents a y-intercept.  The y-intercept of the line is at the point (0, 12).  We also notice a zero in the coordinate pair (4, 0).  In this case, the y-coordinate is zero, so this is the x-intercept.  The line crosses the x-axis at the point (4, 0). 

Determining Intercepts from an Equation

How can we use the equation of a line to find its x– and y– intercepts?  A common form of a line is in slope-intercept form: y = mx+b.  This form is called slope-intercept form, because b represents the y-coordinate of the y-intercept (and we know that its x-coordinate is 0).  We can also use the equation in this form to find the x-intercept.  Since x-intercepts have a y-coordinate of 0, we set the equation equal to zero and solve for x.  This is shown in the example below: 


Terms to Know

the location on a graph where a line or curve intersects the x-axis: (x, 0)


the location on a graph where a line or curve intersects the y-axis: (0, y)