Question

Delia is a graphic designer who charges an hourly rate. She made the graph to show her total earnings for various numbers of hours worked. Approximately how many hours would it take Delia to earn $250?

Answer 1

approximately 7 hours

see the explanation

Explanation:

The picture of the question in the attached figure

Let

x ----> the time worked in hours

y ----> the amount earning in dollars

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so

In this problem we have a proportional relationship

step 1

Find approximately how many hours would it take Delia to earn $250 ?

Looking at the graph

For y=$250 The value of x is approximately 7 hours

see the attached figure N 2

step 2

Find the exact value

from the graph take the point (5,175)

Find the value of k

`k=(y)/(x)` ---->
`k=(175)/(5)=\$35\ per\ hour`

The linear equation is

`y=35x`

For y=$250

substitute

`250=35x`

solve for x

`x=7.14\ hours`