A contractor charges a flat rate plus a fixed rate per hour to come and...

The contractor charges a flat rate plus a fixed rate per hour, so this situation is modeled by a linear function:

C(t)=mt+b

where:

m= " hourly rate "

and

b= " flat rate "

We are given two points:

(3│220)

and

(5│340)

These mean:

A 3-hour job costs $220.

A 5-hour job costs $340.

First, find the hourly rate using slope:

m=(340-220)/(5-3)

m=120/2

m=60

So the contractor charges:

$60 " per hour "

Now the function has the form:

C(t)=60t+b

Use the point (3│220)to find the flat rate:

220=60(3)+b

220=180+b

b=40

So the function is:

C(t)=60t+40

Check with t=5:

C(5)=60(5)+40

C(5)=300+40

C(5)=340

This matches the given information.