Topic 4.3 (Graphing Inequalities)

To graph an inequality, graph the equality (straight line) first and then pick          

a coordinate point (usually (0, 0)). If this point shows a true statement

you shade the area (half plane) including the point. If this point shows a

false statement you shade the area that doesn’t contain the point.

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Sample problem

     Graph the inequality                 y £ x + 2            on the grid below.

     First graph the equality             y = x + 2

                                                        m = 1/1,              b = 2

After the straight line is shown, substitute the point(0, 0) into the original

inequality.    y £ x + 2,   (0, 0),   0 £ 0 + 2,   0 £ 2, true - shade down

and to the right (including the point).  Remember the straight line is a

solid line because of less than or equal to(£ )in the problem.

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      Graph the inequality                   3x - 2y > 12.

      Solve the equation for y and graph.

                         3x - 2y = 12                        This gives the straight line.

                               -2y = -3x + 12

                                   y = (3/2) x -6         m = 3/2           b = -6

Draw the straight line. In this case it will be a broken (open) line because

of the greater than(>). This symbol does not contain the equal, so the

straight line is not solid.

Substitute the point (0, 0) into the original inequality.

            3x - 2y > 12,     (0, 0),      3(0) - 2(0) > 12,    0 - 0 > 12,    0 > 12,    False

Shade down and to the right or the region than doesn’t include the

point.

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Graph  the following inequality.

             x + y ³ 5,        y = -x + 5              Solve for y (y = mx + b).

                m = -1/1,           b = 5              Find the slope and the y-intercept.

The straight line will be solid, because of the greater than or equal to(³ )

Substitute (0, 0) into the inequality   0 + 0 ³ 5,   0 ³ 5,   False Shade up

and to the right (the region not including the point). Please notice:  the region

shaded is:  x  +  y  > 5,  the solid line is: x  +  y  =  5, and the region to the left and

down is:  x  +  y  <  5