A local aquarium found that if the price of admission was $8, the attendance was about 1150 customers per

Question

A local aquarium found that if the price of admission was $8, the attendance was about 1150 customers per week. When the price of admission was dropped to $5, attendance increased to about 1750 per week. Write a linear equation for the attendance in terms of the price, p. ( A=mp+b )

Answer 1

Hey Michelle! 

 

Because the question asks for a linear equation, I know I want to figure out what my slope is going to be! This is the way I do that: 

 

I need to find the independent variable (x) and the dependent variable (y). The information in the word problem helps me to do this! 

 

When the price of admission was $8, the attendance was 1150 -> when (x), (y)... The independent variable (x) is price and the dependent variable (y) is attendance! 

So let's find the ordered pairs we need to find the slope: 

 

(price, attendance) -> (8,1150) and (5,1750) 

We use this equation to solve for m or slope: (y₂ - y₁)/(x₂ - x₁) -> (600 / -3)

                                                 Simplify this

                                                           ↓
So far my equation looks like: A = (600/-3)x + b

 

To solve for b, I just use one of my ordered pairs!

 

The full equation should be: A = -200x + 2750

 

Hope this helps!