Landscape Design
Landscape designers often use coordinate geometry and algebra as they help their clients. In many regions, landscape design is a growing field. With the increasing popularity of do-it-yourself television shows, many homeowners are becoming amateur landscape artists.
Imagine you are a homeowner getting ready to sell your home. You realize there are some landscaping problems you want to address so your home will sell quickly and you can get the best price. After making this decision, you realize there are many things to consider when landscaping the backyard, such as budget, time, and space.Application Practice
Answer the following questions. Use Equation Editor to write mathematical expressions and equations. Click the white space below each question to maintain proper formatting.
1. You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project.
a. Write an inequality that demonstrates how much money you are willing to spend on the project.
b. For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 30 tons of rock to cover the area. If each ton costs $60 and each tree is $84, what is the maximum number of trees you can buy with a budget of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
c. Would five trees be a solution to the inequality in Part b? Justify your answer.
2. The coordinate graph of the backyard shows the location of the trees, plants, patio, and utility lines. If necessary, you may copy and paste the image to another document and enlarge it.
a. What are the coordinates of Tree A, Plant B, Plant C, Patio D, Plant E, and Plant F?
b. The water line is given by the equation
Imagine you want to put a pink flamingo lawn ornament in your backyard. You want to avoid placing it directly over the water line in case you need to excavate the line for repairs in the future. Could you place it at the point (-4,-10)?
c. What is the slope and y-intercept of the line in Part b? How do you know?