Question

Key Club hosted a fundraising event where the profit they made depends on the number of people. If 100 people attend they make $2500. If 80 people attend they make $1500.

like can someone help me please?

Answer 1

The linear equation that represent this problem is
`y=50x-2,500`

Explanation:

Let

x -----> the number of people

y ----> the profit in dollars

we have

For x=100, y=2,500

and

For x=80, y=1,500

Find the slope m

we have

(80,1,500) and (100,2,500)

The slope is equal to

`m=(2,500-1,500)/(100-80)\\ \\m=50(\$)/(people)`

Find the equation of the line into point slope form

`y-y1=m(x-x1)`

we have

`m=50` and point (100,2,500)

substitute

`y-2,500=50(x-100)` ----> equation in slope point form

Convert to slope intercept form

`y=50x-5,000+2,500`

`y=50x-2,500`