Question

A local theme park found that if the price of admission was $12 per person, the attendance for the week was 2200. When the price of admission was lowered to $10, the attendance rose to 3000 for the week. Write a linear equation for the attendance in terms of the price.

Answer 1

You have two points

(12,2200) and (10,3000) You have enough information to set up an equation.

x1 = 12

x2 = 10

y1 = 2200

y2 = 3000

The slope = (y2 - y1)/ (x2 - x1)

The slope = (3000 - 2200) / (10 - 12)

Slope = 800 / - 2

slope = - 400

So far what you have is y = - 400x + b

To get b just use one of the points.

(10,3000)

y = - 400x + b

3000 = -400*10 + b

3000 = - 4000 + b Add 4000 to both sides.

3000 + 4000 = b

b = 7000

Answer y = - 400x + 7000

What happens if you use (12,2200)

y = -400*12+ 7000

y = - 4800 + 7000

y = 2200 As it should.