Graphing Linear Inequalities on a Coordinate Plane

Graphing Linear Inequalities on a Coordinate Plane

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

Example 1

Graph the given linear inequality on the coordinate plane. y > x + 2

[ > ] 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

Graph the given linear inequality on the coordinate plane. y <= -3x + 4

[ ≤ ] does include [ = ].

So use a solid line
to draw y = -3x + 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 [ ≤ ] -3x + 4)

So color the lower region of the solid line.

This is the answer.

Example 3

Graph the given linear inequality on the coordinate plane. y < 1

[ < ] 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

Graph the given linear inequality on the coordinate plane. x >= -2.

[ ≥ ] 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.