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) = 7x - 25, 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? Check all that apply. A. She will lose $7 per week if she does not knock on any doors. B. She can earn $7 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 $25. D. Her expenses are $25 per week.

Answer 1

The correct interpretations of the y-intercept in Jessica's function, E(x) = 7x - 25, are that if she does not knock on any doors during the week, she will lose $25, and this loss represents her weekly expenses.

Step-by-step explanation:

The question revolves around interpreting the y-intercept of a linear function representing Jessica's weekly earnings from selling books. The given function is E(x) = 7x - 25, where 'x' represents the number of doors knocked on and E(x) is the earnings in dollars. To understand the y-intercept, we must evaluate the function at x=0, which is the scenario when Jessica does not knock on any doors.

By substituting x=0 into the equation, we get E(0) = 7(0) - 25, which simplifies to E(0) = -25. This means that Jessica will have a negative earning or a loss of $25 when she does not make any sales during the week. Hence, this represents her weekly expenses. Therefore, the reasonable interpretations of the y-intercept are:

• C. If she does not knock on any doors at all during the week, she will lose $25.
• D. Her expenses are $25 per week.

Options A and B are incorrect because they suggest that Jessica would either lose or earn $7 per week regardless of knocking on doors, which is not supported by the given function.

Answer 2

Her expenses are $25 per week.

Step-by-step explanation:

Given :Jessica earns a commission on each sale but has to pay for her own expenses.

She writes the equation of the function like this:
`E(x) = 7x - 25`, where x is the number of doors she knocks on during the week and 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:

`E(x) = 7x - 25`

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

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

Calculate y intercept

Substitute x = 0

`y= - 25`

Since E(x) is her total earning after clearing the payment of all her expenses.

So, 25 is her expenses per week.

Since we are given that she need to pay her expenses .

So, if there is no sale , still she need to pay expenses.

Thus the reasonable interpretations of the y-intercept of Jessica's function is Her expenses are $25 per week.