Axia College Material
Appendix D
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 will are willing to spend on the
project.
6000 ≤ 𝑥 ≤ 10000
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.
2500 ≥ (60 ∗ 30) + 84𝑥
2500 − 1800 ≥ 84𝑥
700 ≥ 84𝑥
8.3 ≥ 𝑥
Since you can’t plant part of a tree, the answer is 8.
c.
Would five trees be a solution to the inequality in Part b? Justify your answer.
Yes. The rock costs $1800 and 5 trees costs $420. Together that is $2200, which is under the
budget.
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.
MAT/116
a. What are the coordinates of Tree A, Plant B, Plant C, Patio D, Plant E, and Plant F?
Tree A: labeled point at (-20, 20), covers square
area from approx ( -24, 20 ) to (-14 , 10 )
Plant B: labeled point at (-20, -4), covers square
area from approx ( -20, -4) to (-16 , -8 )
Plant C: labeled point at (-10, -14), covers
square area from approx ( -10, -14) to (-6 ,-18 )
Patio D: labeled point at (12, 12), covers square
area from (8 ,18 ) to (18 , 4)
Plant E: labeled point at (8,-8), covers square
area from approx (8 , -8) to ( 12, -12)
Plant F: labeled point at (18, -12), covers square
area from approx (16 , -12) to ( 20,-16 )
b. The water line is given by the equation
2
y   x  12
3
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)?
Check to see if -4, -10 is a solution to the equation
2
−10 = − (−4) − 12
3
−10 + 12 = 8/3
2 = 2.67
Since the given point is not a solution to the equation, the flamingo will not be directly over the
water line.
c.
What is the slope and y-intercept of the line in Part b? How do you know?
The line is in slope intercept form. The slope is -2/3, because that’s the coefficient of the x term. The
constant (-12) is the y-intercept.
d. Imagine you want to add a sprinkler system and the location of one section of the sprinkler line
can be described by the equation
y
1
x4
2
Complete the table for this equation.
x
-6
y
-1
(x,y)
(-6,-1)
MAT/116
-2
0
2
8
-3
-4
-5
-8
(-2,-3)
(0,-4)
(2,-5)
(8,-8)
e. What objects might be in the way as you lay the pipe for the sprinkler?
f.
3. Plants E and F
MAT/116