Question

As an image consultant, Antonio is well paid by his celebrity clients. For 20 hours of work, his fee is $1625. He charges $3500 for 45 hours of his time. Express his fee in terms of his hourly rate. What is the fee for 40 hours of his time?

Answer 1

The fee for 40 hours of his time is $3,125

Explanation:

Let

x -----> the number of hours

y ----> the amount in dollars of Antonio;s fee

we have

For x=20, y=1,625 -----> ordered pair (20,1,625)

For x=45, y=3,500) ----> ordered pair (45,3,500)

Find the linear equation

step 1

Find the slope of the line m

The slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values

`m=(3,500-1,625)/(45-20)`

`m=(1,875)/(25)=75\ \$/h`

step 2

Find the equation of the line in point slope form

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

we have

`m=75` and
`point(20,1,625)`

substitute

`y-1,625=75(x-20)`

Convert to slope intercept form

`y=75x-1,500+1,625`

`y=75x+125`

Determine the fee for 40 hours of his time

For x=40 h

substitute in the equation

`y=75(40)+125=\$3,125`