IM Alg1.2.22 Lesson: Graphing Linear Inequalities in Two Variables (Part 2)
A homeowner is making plans to landscape her yard.
Write an equation that represents the square feet of grass sod, , and the square feet of flower beds, , that she could afford if she used her entire budget.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. 
On the coordinate plane, sketch a graph that represents your equation. Be prepared to explain your reasoning.
The homeowner is worried about the work needed to maintain a grass lawn and flower beds, so she is now looking at some low-maintenance materials.
The graph shows a line going through . In this situation, what does the point mean?
Write an equation that the line represents.
What do the solutions to the equation mean?
The point is located to the right and above the line. Does that combination of turf and gravel meet the homeowner’s constraints? Explain or show your reasoning.
Choose another point in the same region (to the right and above the line). Check if the combination meet the homeowner’s constraints.
The point is located to the left and below the line. Does that combination of turf and gravel meet the homeowner’s constraints? Explain or show your reasoning.
Choose another point in the same region (to the left and below the line). Check if the combination meets the homeowner’s constraints.
A vendor at the Saturday Market makes $9 profit on each necklace she sells and $5 profit on each bracelet.
Find a combination of necklaces and bracelets that she could sell and make:
Write an inequality that represents the constraints in this situation. Explain what the solutions mean and show the solution region on the graph.
Click to highlight the solution region on the graph.
Write an equation whose solution is the combination of necklaces and bracelets she could sell and make exactly $100 profit.
Write an inequality whose solutions are the combinations of necklaces and bracelets she could sell and make more than $100 profit.
Graph the solutions to your inequality.
Is a solution to the inequality? Explain your reasoning.
Write an inequality using two variables and where the solution would be represented by shading the entire coordinate plane.
Write an inequality using two variables and where the solution would be represented by not shading the entire coordinate plane.
A popular band is trying to raise at least $20,000 for charity by holding multiple concerts at a park.
It plans to sell tickets at $25 each. For each 2-hour concert, the band would need to pay the park $1,250 in fees for security, cleaning, and traffic services. The band needs to find the combinations of number of tickets sold, , and number of concerts held, , that would allow it to reach its fundraising goal. Write an inequality to represent the constraints in this situation.
Graph the solutions to the inequality on the coordinate plane.
Name two possible combinations of number of tickets sold and number of concerts held that would allow the band to meet its goal.
Which combination of tickets and concerts would mean more money for charity: