Linear Inequality (Two Variables)

How to graph a linear inequality on a coordinate plane: 4 examples and their solutions.

Example 1

Example

Solution

Prepare to draw y = x + 2.

Slope-Intercept Form

Start from the y-intercept 2.

The slope is 1.
So move 1 unit to the right.
And move 1 unit upward.
Mark this endpoint.

The inequality sign does not include [=].

So draw a dashed line
that passes through
the y-intercept and the marked endpoint.

See the given inequality.
y is greater than the right side.

So color the upper region of the dashed line.

So this colored region, excluding the line, is the answer.

Example 2

Example

Solution

Prepare to draw y = 3x - 4.

Start from the y-intercept -4.

The slope is 3.
So move 1 unit to the right.
And move 3 units upward.
Mark this endpoint.

The inequality sign does include [=].

So draw a solid line
that passes through
the y-intercept and the marked endpoint.

See the given inequality.
y is less than (or equal to) the right side.

So color the lower region of the solid line.

So this colored region, including the line, is the answer.

Example 3

Example

Solution

Point y = 1 on the y-axis.

The inequality sign does not include [=].

So draw a horizontal dashed line
that passes through y = 1.

See the given inequality.
y is less than the right side.

So color the lower region of the dashed line.

So this colored region, excluding the line, is the answer.

Example 4

Example

Solution

Point x = -2 on the x-axis.

The inequality sign does include [=].

So draw a vertical solid line
that passes through x = -2.

See the given inequality.
x is greater than (or equal to) the right side.

So color the right region of the solid line.

So this colored region, including the line, is the answer.