Graphing Linear Inequalities

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SWBAT represent the solution to a linear inequality on the coordinate plane.

Big Idea

Students will combine their knowledge of inequalities and linear functions to graph solution sets.


10 minutes

Students will complete the Do Now in 5 minutes. I will then ask six volunteers to come up to the board to draw a sketch on their graph for the class.

A student will then read the objective, "SWBAT represent the solution to a linear inequality on the coordinate plane."

I will ask students to recall what we learned during our last class, and to think about how our previous objective can be translated to a coordinate plane.

Guided Notes + Practice

30 minutes

For today's direct instruction, students will follow along using these Guided Notes. Before I begin, I will ask my students to use the table at the top of their notes to write down the four inequality symbols and their corresponding symbol on a number line (shaded circle or unshaded circle).

We will start off by graphing the line y > 3x - 4 the same way y = 3x - 4 would be graphed. I will then ask students to recall what we learned about inequalities during our last class. After they share some ideas I will ask:

How does the presence of an inequality symbol in our current example effect the graph of the solution?

Eventually I will say, "Since inequalities represent situations where there are multiple solutions, let's figure out which side of our graph is true, and which side is false."

Since I have now set up a comparison, I will ask a student to identify out points on the graph as coordinates, one on each side of the line. Then, we will work as a class to test the points by plugging them into the original inequality. After each test, we will label the points on the graph using the word true or the word false. We will repeat this process multiple times until it is evident that all of the true solutions only lie on one side of the graph. We will then shade the entire side of the plane that contains true values.

Before we graph our next example, 2x + 3, I will ask students to describe the difference between these two symbols: , <. We will discuss this until the information we need to correctly graph the relation is identified, but I will not specifically point out that we will be making the line solid, rather than dotted. I'd love it if my students made this observation first. 

We will follow the same process as the previous example. Since the solution to y < 2x + 3 will not include values that make y = 2x + 3 true, we will represent this graph using a dashed line. At this point I will introduce the word boundary line, and ask students to add solid and dashed lines to the table at the top of their notes below the corresponding inequality symbols.

Independent Practice

30 minutes

Students will continue to practice today's objective using this Kuta Software handout. Students can choose to work independently or with a partner, but will be required to compare their work with a peer every 10 minutes. We will then review our responses as a whole group.


10 minutes

To close, I will ask the group to decide if the test point chosen in a linear inequality can also lie on the boundary line. I will ask a few students to justify their response with an example or counterexample on the board.

Students will then complete an Exit Card.