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.  [br][br]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.[br][br]Here is a graph representing some constraints in this situation. [br][br][img]data:image/png;base64,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[/img][br][br]The graph shows a line going through (500, 100).[br][br]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. [br][br]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. [br][br]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. 
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Information: A.2.22.2 Rethinking Landscaping