Section 7.8A

Graphing Technology

Graphing Inequalities

This is a preview of Lesson 7-8

Inequalities in two variables can be graphed on a graphing calculator using the "Shade(" command, which is option 7 on the DRAW menu. You must enter two functions to activate the shading since the calculator always shades between two specified functions. The first function entered defines the lower boundary of the region to be shaded. The second function defins the upper boundary of the region. The calculator graphs both functions and shades between the two.

Example 1: Graph y2x - 3 in the standard viewing window.

The inequality refers to points at which y is greater than or equal to 2x - 3. This means we want to shade above the graph of y = 2x - 3. Since the calculator screen shows only part of the coordinate plane, we can use the top of the screen, Ymax or 10, as the uppper boundary and 2x - 3 as the lower boundary.

ENTER: 7 2 - 3 , 10 )

Since both the x- and y-intercepts of the graph and the origin are within the current viewing window, the graph of the inequality is complete.

Example 2: Graph y - x1 in the standard viewing window.

First solve the inequality for y: yx + 1. This inequality refers to points where y is less than or equal to x + 1. This means we want to shade below the graph of y = x + 1. We can use the bottom of the screen, Ymin or -10, as the lower boundary and x + 1 as the upper boundary.

ENTER: 7 - 10 , + 1 )

For Practice: Do 7-8 A Exercises