To graph linear inequalities given in standard form, convert to slope-intercept form, then determine the y-intercept and the slope and graph:

Example 1

Graph 4x + 5y ≥ 15

To convert this example to slope-intercept form, subtract 4x from both sides of the inequality.

Then, divide all terms by 5.

4x + 5y ≥ 15
- 4x      - 4x
5y ≥ - 4x + 15
y ≥ – 4 5 x + 3
y-intercept: 3
slope: – 4 5

In slope-intercept form, the inequality is:

y ≥ – 4 5 x + 3

Since the inequality symbol is ≥, draw a solid line and shade above the line.

Example 2

Graph x – 3y > 9.

To convert this example to slope-intercept form, subtract x from both sides of the inequality.

Then, divide all terms by -3. When an inequality is divided by a negative, the symbol changes between < and > or ≤ and ≥.  In this case, the symbol changes from > to <.

x – 3y > 9

-x        -x

-3y > -x + 9

y < 1 3 x – 3

y-intercept: -3

slope: 1 3

In slope-intercept form, the inequality is:

y < 1 3 x – 3

Since the inequality symbol is <, draw a dashed line and shade below the line.