Concept Byte: Graphing Linear Inequalities

Use With Lesson 6-6

TECHNOLOGY

A graphing calculator can show the solutions of an inequality or a system of inequalities. To enter an inequality, press apps begin box , apps , end box  and scroll down to select INEQUAL. Move the cursor over the = equals  symbol for one of the equations. Notice the inequality symbols at the bottom of the screen, above the keys labeled F2–F5. Change the = equals  symbol to an inequality symbol by pressing alpha begin box , alpha , end box  followed by one of F2–F5.

ACTIVITY 1

Graph the inequality y < 3 x − 7 . bold italic y less than 3 bold italic x minus 7 .

1. Move the cursor over the = equals  symbol for Y 1 . cap y sub 1 , .  Press alpha begin box , alpha , end box  and F 2 cap f 2  to select the < less than  symbol.
2. Enter the given inequality as Y 1 . cap y sub 1 , .
3. Press graph begin box , graph , end box to graph the inequality.

ACTIVITY 2

Graph the system.

y − 2 x − 3 y ≥ x + 4 table with 2 rows and 1 column , row1 column 1 , bold italic y minus 2 bold italic x minus 3 , row2 column 1 , bold italic y greater than or equal to bold italic x plus 4 , end table

4. Move the cursor over the = equals  symbol for Y 1 . cap y sub 1 , .  Press alpha begin box , alpha , end box  and F2 to select the < less than  symbol. Enter the first inequality as Y 1 . cap y sub 1 , .
5. Then move the cursor over the = equals  symbol for Y 2 , cap y sub 2 , comma  and press alpha begin box , alpha , end box  and F5 to select the ≥ greater than or equal to  symbol. Enter the second inequality as Y 2 . cap y sub 2 , .
6. Press graph begin box , graph , end box  to graph the system of inequalities.

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Exercises

Use a graphing calculator to graph each inequality. Sketch your graph.

7. y ≤ x y less than or equal to x
8. y > 5 x − 9 y greater than 5 x minus 9
9. y ≥ − 1 y greater than or equal to , minus 1
10. y < − x + 8 y less than minus . x plus 8

Use a graphing calculator to graph each system of inequalities. Sketch your graph.

11. y ≥ − x + 3 y greater than or equal to negative x plus 3

    y ≤ x + 2 y less than or equal to x plus 2

12. y > x y greater than x

    y ≥ 2 x + 5 y greater than or equal to 2 x plus 5

13. y ≥ − 1 y greater than or equal to , minus 1

    y < 0.5 x − 2 y less than 0.5 x minus 2

14. y ≥ 2 x − 2 y greater than or equal to 2 x minus 2

    y ≤ 2 x − 4 y less than or equal to 2 x minus 4

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