Graphing Linear Inequalities in Two Variables
The Lesson Activities will help you meet these educational goals:
· Mathematical Practices—You will make sense of problems and solve them, reason abstractly and quantitatively, and use mathematics to model real-world situations.
· Inquiry—You will analyze results and draw conclusions.
· STEM—You will apply mathematical and technology tools and knowledge to analyze real-world situations.
· 21st Century Skills—You will employ online tools for research and analysis.
Directions
Save this document before beginning the lesson and keep the document open for reference during the lesson. Type your answers directly in this document for all activities.
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Self-Checked Activities
Read the instructions for the following activities and type in your responses. At the end of the lesson, click the link to open the Student Answer Sheet. Use the answers or sample responses to evaluate your own work.
1. Graphing Linear Inequalities in Two Variables
a. Betty's bakery bakes white bread and brown bread. The loaves of bread are then stored in a store room that can house only 900 loaves. The loaves are baked during the day, and in the evening they are delivered to convenience stores. At all times, the number of loaves in the store room must be less than or equal to 900.
1. Assuming x to be the number of loaves of white bread and y to be the number of loaves of brown bread, how would the problem be represented in the form of an inequality?
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2. Represent the inequality in the form of a graph. Replace the inequality sign with an equal sign for this activity. Use the provided coordinate plane to draw the graph.
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3. Plug in a test point to find the region to be shaded on the graph. Find a test point that holds true for the inequality.
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4. Looking at the test point, which region of the graph must be shaded?
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5. Represent the inequality on the provided coordinate plane, and shade the correct region.
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6. In this scenario, what do the negative numbers represent? Should the negative regions of the graph be shaded, given the problem? If necessary, change the shaded region of the graph to reflect your response.
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b. Sixth-grade students at Cramon Junior High are not to have more than 12 hours of homework per week. They take one math course and two science courses in sixth grade. The amount of time required to do homework for a math course is x hours, and the time required to do homework for a science course is y hours.
1. How would this problem be represented in the form of an inequality?
Type your response here:
2. Represent the inequality on the provided coordinate plane. Replace the inequality sign with the equal sign for this activity.
Type your response here:
3. Plug in a test point to find the region to be shaded on the graph. Find a test point that holds true for the inequality.
Type your response here:
4. Looking at the test point, which region of the graph must be shaded?
Type your response here:
5. Represent the inequality on the provided coordinate plane, and shade the correct region.
Type your response here:
6. In this scenario, what do the negative numbers represent? Should the negative regions of the graph be shaded, given the problem? Change the shaded region of the graph based on your answer.
Type your response here:
How did you do? Check a box below.
Nailed It!—I included all of the same ideas as the model response on the Student Answer Sheet.
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