# After School Job

# After School Job

Ashley is trying to find an after school job, but her mother is concerned that it will interfere with her practicing her clarinet. She calculated that she has at most 30 hours a week available for both clarinet practice and work. In addition, she has decided that she should practice her clarinet at least twice as many hours as she works.

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Card Sort Activity**Reflection Question**

- How can we describe all the choices that meet Ashley’s criteria?

In the next section, we will look at linear inequalities to help us answer that question.

# Graphing Linear Inequalities

# Graphing Linear Inequalities

Let's look more closely at Ashley's situation. We can define *x* as the number of hours she spends practicing the clarinet each week and define *y* as the number of hours she spends working each week.

First, we know that Ashley cannot use more than a total of 30 hours for both activities each week. We can use the inequality *x* + *y* ≤ 30 to represent this constraint.

We also know that Ashley wants to practice the clarinet at least twice as many hours as she is working each week. We can use the inequality *x* ≥ 2*y* to represent this constraint.

Before you can use the graphing utility to show both of the inequalities, you must solve both equations for *y*.

Graph both inequalities in the graphing utility. (**Note**: you may have to adjust your window.)

- Use a semi-colon to separate the functions.
- Press the SET FUNCTION button.
- Choose the appropriate inequality symbol for each.

Notice that the graph is divided into four color-coded sections.

- The blue shaded area represents points that would make the blue inequality true.
- The red shaded area represents points that would make the red inequality true.
- The purple shaded area represents points that would make
**both**inequalities true. - The unshaded area (white) represents points that would make neither inequality true.

# Practice Graphing Systems of Linear Inequalities

# Practice Graphing Systems of Linear Inequalities

The solution to a system of linear inequalities consists of all the points in the area of the coordinate plane that satisfies both inequalities.

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Matching Activity