x-intercept, y-intercept

x-intercept, y-intercept

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

Definition

x-intercept: the intersection between the graph and the x-axis. y-intercept: the intersection between the graph and the y-axis.

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

Find the x-intercept and the y-intercept of the given line.

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

Find the x-intercept of the given linear equation. 3x + 4y = 12

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:
3x + 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

Find the y-intercept of the given linear equation. 3x + 4y = 12

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 + 4y = 12.

Solve the equation.
Then y = 3.

So the y-intercept is 3.

Linear equations (One variable)

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