Shading Graphs

To shade a graph, you must first graph the function.

To do this you must first have the function in the form of y = . Remember when working with inequalities you flip the inequality if you ever multiply or divide by a negative number.

Enter the function into the graphing window.

Example: Graph the feasible region.

$2x - 3y \geq -12$

Solve the inequality for y.

$y \leq \frac{(-2x-12)}{-3}$

Note: There is no need to simplify the function beyond this since we are using the calculator to graph.

Enter the function into the calculator and graph using the standard window.

The screen on the left is the Y= menu and the screen on the right is the Window Menu, and the graph.

Now move the cursor to the diagonal to the left of Y₁ and choose the desired shading by repeatedly pressing . The style of shading is determined by the inequality that was solved for y. Lower shading is used when the inequality is < and upper shading is when the inequality is >.

The symbols for lower shading is seen beside the Y₄ and the symbol for upper shading is seen beside Y₃ in this screen.

The next two screens show lower shading selected for our function and then the graph when the button is pressed.

Graphing more than one inequality

Example: Find the feasible region for this system of inequalities.

$2x - 3y \geq -12$

$x + y \geq 10$

The screens show the results when using the method given above to graph both inequalities at the same time. The actual answer that you would show on your paper is the region that is shaded by both inequalities. Notice that more inequalities makes the screen more difficult to read.

Reverse Shading Method

The reverse shading method is to have the calculator shade the parts that you don't actually want. The advantage of this is that in the final graph, the region that is not shaded is the feasible region. The screens show the results when using reverse shading.