Question

Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her own expenses.

After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on.

She writes the equation of the function like this: E(x) = 20x - 50, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars.

Which of the following are reasonable interpretations of the y-intercept of Jessica's function?

a. She will lose $20 per week if she does not knock on any doors.

b. She can earn $20 per week even if she does not knock on any doors

c. If she does not knock on any doors at all during the week, she will lose $50

d. Her expenses are $50 per week

Answer 1

Her expenses are $50 per week

Explanation:

Given :
`E(x) = 20x - 50`

x is the number of doors she knocks on during the week

E(x) is her earnings for the week in dollars.

To Find:Which of the following are reasonable interpretations of the y-intercept of Jessica's function?

Solution:

We are given that Jessica earns a commission on each sale but has to pay for her own expenses.

So, Expenses will be deducted from the total earning every week whether she earns anything or not.

Now we are given that function for total cost per week :
`E(x) = 20x - 50`

So, For y intercept , substitute x= 0

`E(x) = 220(0) - 50`

`E(x) = - 50`

So, her expenses per week is 50

So, - 50 denotes the deduction of expenses

Thus Option D is correct.

Her expenses are $50 per week

Answer 2

D) Her expenses are $50 per week.

This is because its $20*the number of doors she knocks on-expenses