# Linear Inequality (Two Variables)

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

## ExampleGraph y > x + 2

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.

## ExampleGraph y ≤ 3x - 4

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.

## Exampley < 1

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.

## Examplex ≥ -2

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.