Question

A deep sea fishing company took a group of 5 fishermen out for $500 and a group of 9 fishermen out for $700. Write an equation that will represent the cost, y, of the trip for x fishermen.

Answer 1

The equation is
`y = 50x + 250`

Explanation:

Linear equation:

A linear equation has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept.

A deep sea fishing company took a group of 5 fishermen out for $500 and a group of 9 fishermen out for $700.

This means that we have these two points:

(5,500) -> When x = 5, y = 500

(9, 700) -> When x = 9, y = 700

Finding the slope:

Given a pair of points, the slope is given by the change in the output(in this case y) divided by the change in the input(in this case x). So

Change in y: 700 - 500 = 200

Change in x: 9 - 5 = 4

Slope:
`m = (200)/(4) = 50`

So

`y = 50x + b`

(5,500) -> When x = 5, y = 500

We use this to find b. So

`y = 50x + b`

`500 = 50*5 + b`

`b = 250`

So

`y = 50x + 250`