The graph of the inequality is the shaded region and boundary of the inequality is . To graph the boundary, find the x-intercept and y-intercept of the line.

First find the y-intercept.

The y-intercept is the value of y, when x = 0.

                          (Substitute x = 0 in original equation)

                             (Apply Additive identity property: 0 – 6y = – 6y)

Apply subtraction property of equality: If a = b than a – c = b – c.

                  (Subtract 3 from each side)

                                (Apply Additive inverse property: 3 – 3 = 0)

Apply division property of equality: If a = b than .

                          (Divide each sige by negative 6)

                                      (Cancel common terms)

                                    (Divide: )

The y-intercept is 0.5, so the graph intersects the y-axis at (0, 0.5).

Next find the x-intercept.

The x-intercept is the value of x, when y = 0.

                       (Substitute y = 0 in original equation)

                                 (Apply zero product property: )

                       (Subtract 3 from each side)

                                     (Apply Additive inverse property: 3 – 3 = 0)

The x-intercept is – 3 , so the graph intersects the x-axis at ( – 3, 0).

To draw inequality follow the steps.

1.   Draw a coordinate plane.

2.  Plot the points.

3.  Since inequality symbol is >, the boundary is not included in the solution set. Graph the boundary of the inequality with a dashed line.

4.  To determine which half-plane to be shaded use a test point in either half-plane. A simple choice is (0, 0).

Substitute and y = 0 in original inequality .

The statement is true.

5.  Since the statement is true, shade the region that contains point (0, 0).

Inequality graph is