# Graphing Linear Inequalities on a Coordinate Plane

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

## Example 1

[ > ] doesn't include [ = ].

So use a dashed line

to draw *y* = *x* + 2.

Slope-intercept form - Example 2

Start from the *y*-intercept: +2.

The slope is 1.

So move 1 unit to the right

and move 1 unit upward.

Let's call this point the 'endpoint'.

Draw a dashed line

that passes through

the *y*-intercept and the endpoint.

*y* [is greater than] the right side.

(*y* [ > ] *x* + 2)

So color the upper region of the dashed line.

This is the answer.

## Example 2

[ ≤ ] does include [ = ].

So use a solid line

to draw *y* = -3*x* + 4.

Slope-intercept form - Example 2

Start from the *y*-intercept: +4.

The slope is -3.

So move 1 unit to the right

and move 3 units downward.

Let's call this point the 'endpoint'.

Draw a solid line

that passes through

the *y*-intercept and the endpoint.

*y* [is lesser than or equal to] the right side.

(*y* [ ≤ ] -3*x* + 4)

So color the lower region of the solid line.

This is the answer.

## Example 3

[ < ] doesn't include [ = ].

So use a dashed line

to draw *y* = 1.

Draw a horizontal dashed line

that passes through the *y*-axis at *y* = 1.

*y* [is lesser than] the right side.

(*y* [ < ] 1)

So color the region

that covers *y* = 0, -1, -2, ... of the dashed line.

This is the answer.

## Example 4

[ ≥ ] does include [ = ].

So use a solid line

to draw *x* = -2.

Draw a vertical solid line

that passes through the *x*-axis at *x* = -2.

*x* [is greater than or equal to] the right side.

(*x* [ ≥ ] -2)

So color the region

that covers *x* = -1, 0, 1, ... of the solid line.

This is the answer.