A.2.22.2 Rethinking Landscaping

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.   She is considering artificial turf, which costs $15 per square foot to install, and gravel, which costs $3 per square foot. She may use a combination of the two materials in different parts of the yard. Her budget is still $3,000. Here is a graph representing some constraints in this situation.  The graph shows a line going through (500, 100). In this situation, what does the point (500, 100) mean?

Write an equation that the line represents.

What do the solutions to the equation mean?

The point (600, 200) 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 (200, 100) 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.