*x*-intercept, *y*-intercept

How to find the x-intecept and the y-intercept from a linear equation: definition, example, and its solution.

## Definition

The *x*-intercept is the intersection

between the graph and the *x*-axis: *a*.

The *y*-intercept is the intersection

between the graph and the *y*-axis: *b*.

## Example 1: from the Graph

The intersection between the line and the *x*-axis

is -2. (green)

So the *x*-intercept is -2.

The intersection between the line and the *y*-axis

is 1. (brown)

So the *y*-intercept is 1.

## Example 2: *x*-intercept from an Equation

The *x*-intercept is the intersection

between the graph and the *x*-axis.

And the *x*-axis is *y* = 0.

So, to find the *x*-intercept,

put *y* = 0 into the given linear equation:

3*x* + 4⋅0 = 12.

Solve the equation.

Then *x* = 4.

This is the *x*-intercept.

So the *x*-intercept is 4.

Linear equations (One variable)

## Example 3: *y*-intercept from an Equation

The *y*-intercept is the intersection

between the graph and the *y*-axis.

And the *y*-axis is *x* = 0.

So, to find the *y*-intercept,

put *x* = 0 into the given linear equation:

3⋅0 + 4*y* = 12.

Solve the equation.

Then *y* = 3.

So the *y*-intercept is 3.

Linear equations (One variable)

Let's see the graph of 3*y* + 4*y* = 12.

The *x*-intercept is 4.

(It's from the last example.)

And the *y*-intercept is 3.

Then draw a line

that passes through these two intercepts.

This is the graph of 3*y* + 4*y* = 12.