Creating an Equation

Question

A fairground holds a maximum of 2000 people.With ticket prices at $25, the average amount of people attending is 700. For every $3 the ticket prices goes down, about 20 more people attend. Write an equation that represents the number of people attending as a function price?

Answer 1

Lets make a table:

So we see we never have to worry about getting to the maximum.

To write an equation, calculate the slope. Pick any two points and use m = (y2 - y1)/x2 - x1)

Then plug that slope (m) and one point, an (x1, y1) (it doesn't matter which point you pick) into the point-slope form of a line:

y - y1 = m(x - x1) and you have an equation. To make it a function as they discuss, we would solve the equation for y then replace "x" with something like "p" for price and replace "y" with something like N(p) because N could stand for Number of people.