Tree Top Fun-Writing Linear Equations

Tree Top Fun

Writing Linear Equations

Have you ever been zip lining?

Tree Top Adventures runs adventure sites with zip lines, swings, rope ladders, bridges, and trapezes. Like every entertainment business, TTF must have a business plan and a way to monitor day-to-day operations, such as operating costs and number of visitors.

Many times this means writing a linear equation.

What information do we need in order to write a linear equation?

Multiple Choice

Tree Top Adventures charges $25 per customer to enter the park. They also have daily operating costs of $500.  Which equation could be used to find the daily profit, P, for n number of customers?

•  $P=500n+25$  
  

•  $P=25n+500$  
  

•  $P=25n-500$  

•  $P=500n-25$  

Equations from a Table

In the previous problem, you wrote an equation from a rate and starting value. What if you were given a table? How could you write the equation?

Group Rates

One operator of a Tree Top Fun franchise suggested the group admission fees in the table to the right. How can we determine if this relationship is linear?

Multiple Choice

What is the rate of change and starting value for this relationship?

• Rate=15; Starting value=60

• Rate=75; Starting value=60

• Rate=15; Starting value=75

• Rate=21; Starting value=75

Multiple Choice

Which of the following equations would describe the group rates table?

• $y=15x-75$

• $y=15x+75$

• $y=60-15x$

• $y=60+15x$

Equations from graphs

What if you were given a graph? How would you find the equation of the line?

Multiple Choice

What is the equation of the graph?

• $y=-\frac{3}{2}x+2$

• $y=\frac{3}{2}x+3$

• $y=-\frac{3}{2}x+3$

• $y=-\frac{2}{3}x+3$

Poll

How are you feeling about writing equations of linear functions?

• I feel great!

• I sort of get it, but need more practice.

• I still don't know what to do.

Multiple Choice

Previously we found that the profit that Tree Top Adventures makes in a day can be calculated using the following equation, where P represents the profit and n is the number of visitors.

 $P=25n-500$  

If there were 120 visitors on Monday, how much profit did Tree Top Adventures make?

• $120

• $2,500

• $3,000

• $24.80

Multiple Choice

We also found that the equation y = 15x + 60 can be used to find the group cost, y, a group would pay with x number of people in their group.

The math club at Blalack takes a group of 16 people to Tree Top Adventures. How much will it cost the math club?

• $300

• $91

• $240

• $975

Multiple Choice

The equation c = 25n can be used to find the cost, c, of n people going to Tree Top Adventures. What does this equation tell us?

• 25 people are going to Tree Top Adventures.

• The total cost to go to Tree Top Adventures is $25

• We do not have enough information to know what this equation means.

• The cost per person is $25. Total cost is $25 times the number of people.

Multiple Choice

How much will it cost for 16 people to visit Tree Top Adventures if they do not use the group rate?

Use the equation: c = 25n

• $300

• $400

• $41

• $150

Multiple Choice

At what number of visitors will the cost to visit Tree Top Adventures be the same for both the individual cost and the group rate?

As a reminder we found these equations:

Individual cost equation: c = 25n

Group cost equation: c = 60 + 15n

• 15 visitors

• 10 visitors

• 6 visitors

• The cost will never be the same.