Curtis is concerned about the diet he is feeding his pet. A nutritionist has recommended that the...

Healthy AnimalsCurtis is concerned about the diet he is feeding his pet.

A nutritionist has recommendedthat the pet’s diet include at least30 grams of protein per day.He also recommends that a pet diet should include at least 16 grams of fat per day.

Curtis’s pet should not eat more than 12 ounce of food per day.

Curtis would like to vary the diet for his pet within these requirements, and needs to know what the choices are.

Curtis’s favorite pet store carries two brands of food:Food A supplies 2 grams of protein and 4 grams

of fat in each ounce.Food G supplies 6 grams of protein and 2 grams of fat in each ounce.

How much of each food should Curtis feed his pet?

1. Choose variables to represent the amount of each type of food Curtis will include in the daily diet. State clearly what the variables represent.

2. Use your variables to write inequalities to describe the constraints of the situation.

Graph the “Protein” Constraint

Graph the “Fat” Constraint

Graph the “Food Limit” Constraint

Curtis goes into the Pet Store to buy a substantial supply of food for his pet.

He sees that Food A costs$2 per pound and that Food B costs $3 per pound.

Since he intends to vary his pet’s diet from day to day anyway, he isn’t especially concerned about how much he buys of each type of food.

Now do the same thing assuming that Curtis spends $50, using the same set of axes.

Suppose that Curtis has $30 to spend. Find several combinations of the two foods that he might buy and plot them on an appropriately labeled graph.

Now do the same thing assuming that Curtis spends $50, using the same set of axes.

What do you notice about your answers to the last two questions?

Algebra 1A6.6 Graphing Inequalities

in Two Variables

Goals for this Lesson•Graph Inequalities on the Coordinate Plane•Solve Problems Involving Linear InequalitiesThis section starts on page 352 in your text.

GRAPH LINEAR INEQUALITIES Like a linear equation with x and y, the solution set of an inequality in two variables is graphed on the coordinate plane.

The solution set of an inequality in two variables is the set of all ordered pairs that satisfy the inequality.

The solution set for an inequality in two variables contains many ordered pairs when the domain and range are the set of real numbers.

You can list some of the solutions, but not all of them.

The graph of all of these ordered pairs fill a region on the coordinate plane called a half-plane. An equation defines the boundary or edge for each half-plane.

Consider the graph of y > 4.

First determine the boundary by graphing y = 4. This is the equation that goes with the inequality.

Since the inequality does not include 4 (y > 4), you don’t really want to include y = 4. How do you show this?

The next step is to decide which half-plane gets the shading. You have to find the “true” side. This side gets the shading. Check a point on each side of the boundary.

Graph y > 4.

Example 1

Graph 12 xy

Example 2

Graph 42 xyExample 3

Graph 123 x

Example 4

Graph 33

1 xy

Example 5

Graph 632 yx

Example 6

What are the variables?

Classwork:Page 356 # 26, 27, 28, 29, 30, 33

Homework:6.6 Skills Practice