1. Graph the inequality from part (a).
Example 4
Writing and Graphing a Linear Inequality
You have 100 pounds of clay to use for making bowls and vases. You need 5 pounds of clay for each bowl and 2 pounds for each vase. a.
Write an inequality describing the possible numbers of bowls and vases that you can make. b.
Graph the inequality from part (a). c.
Give three possible combinations of bowls and vases that you can make.

2. Example 4
Writing and Graphing a Linear Inequality
SOLUTION a.
Let x be the number of bowls you make. Let y be the number of vases you make. Write a verbal model. Then use the verbal model to write an inequality.
100 2y 5x + ≤

3. Test the point 0, 0 in the inequality. ( )
Example 4
Writing and Graphing a Linear Inequality b.
To graph the inequality, first draw the boundary line Use a solid line because the inequality symbol is ≤.
100 2y 5x + =
Test the point 0, 0 in the inequality. ( )
100 2y 5x + ≤ ( )
100 2 5 + ? ≤
100 ≤

4. Because 0, 0 is a solution, all solutions of
Example 4
Writing and Graphing a Linear Inequality
Because 0, 0 is a solution, all solutions of
lie in the half-plane containing 0, 0 . Shade the portion of this half-plane that lies in the first quadrant, as the numbers of bowls and vases made must be nonnegative. ( )
100 2y 5x + ≤ ( )
Choose three points on the graph with whole-number coordinates, such as 5, 20 , 10, 10 , and
20, 0 . You can make 5 bowls and 20 vases, or 10 bowls and 10 vases, or 20 bowls and no vases. c. ( )

5. Checkpoint 4.
It is recommended that you get at least 60 milligrams of vitamin C each day. One fluid ounce of orange juice contains about 15 milligrams of vitamin C, and one fluid ounce of grapefruit juice contains about 12 milligrams. Write and graph an inequality describing the possible amounts of orange juice and grapefruit juice you can drink to meet your daily requirement for vitamin C.

6. Checkpoint
ANSWER
Let x be the amount of orange juice and y be the amount of grapefruit juice (both in fluid ounces). Then . 60
12y
15x + ≥