Graphing Linear Inequalities in Two Variables (Part 2)
5 min
Narrative
In this lesson, students will be writing linear inequalities that represent constraints in situations and graphing the solution regions. To prepare for that work, students review writing and graphing an equation that represents a situation.
Launch
If needed, explain or show additional images of grass sod and flower beds to students who might be unfamiliar with these landscaping terms.
Student Task
A homeowner is making plans to landscape her yard. She plans to hire professionals to install grass sod in some parts of the yard and flower beds in other parts.
Grass sod installation costs $2 per square foot, and flower bed installation costs $12 per square foot. Her budget for the project is $3,000.
- Write an equation that represents the square feet of grass sod, x, and the square feet of flower beds, y, that she could afford if she used her entire budget.
- On the coordinate plane, sketch a graph that represents your equation. Be prepared to explain your reasoning.
Sample Response
- 2x+12y=3,000 (or equivalent)
- Sample response:
Activity Synthesis (Teacher Notes)
Invite students to share their equation and graph. Discuss with students:
- "In this situation, what does a point on the line mean?" (A combination of square feet of grass sod and square feet of flower beds that the homeowner could have if she spent her entire budget.)
- "What does the vertical intercept of the graph mean?" (The square feet of flower beds she could have if she installs no grass sod.)
- "What does the horizontal intercept of the graph tell us?" (The square feet of grass sod she could install if she installs no flower beds.)
Standards
Addressing
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-REI.10·Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- A-REI.10·Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- A-REI.10·Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- HSA-CED.A.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <span>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</span>
- HSA-REI.D.10·Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
20 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Graphing Linear Inequalities in Two Variables (Part 2)
5 min
Narrative
In this lesson, students will be writing linear inequalities that represent constraints in situations and graphing the solution regions. To prepare for that work, students review writing and graphing an equation that represents a situation.
Launch
If needed, explain or show additional images of grass sod and flower beds to students who might be unfamiliar with these landscaping terms.
Student Task
A homeowner is making plans to landscape her yard. She plans to hire professionals to install grass sod in some parts of the yard and flower beds in other parts.
Grass sod installation costs $2 per square foot, and flower bed installation costs $12 per square foot. Her budget for the project is $3,000.
- Write an equation that represents the square feet of grass sod, x, and the square feet of flower beds, y, that she could afford if she used her entire budget.
- On the coordinate plane, sketch a graph that represents your equation. Be prepared to explain your reasoning.
Sample Response
- 2x+12y=3,000 (or equivalent)
- Sample response:
Activity Synthesis (Teacher Notes)
Invite students to share their equation and graph. Discuss with students:
- "In this situation, what does a point on the line mean?" (A combination of square feet of grass sod and square feet of flower beds that the homeowner could have if she spent her entire budget.)
- "What does the vertical intercept of the graph mean?" (The square feet of flower beds she could have if she installs no grass sod.)
- "What does the horizontal intercept of the graph tell us?" (The square feet of grass sod she could install if she installs no flower beds.)
Standards
Addressing
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-CED.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <em>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</em>
- A-REI.10·Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- A-REI.10·Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- A-REI.10·Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- HSA-CED.A.3·Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. <span>For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.</span>
- HSA-REI.D.10·Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).