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mylen
15 days ago
6

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.
Mathematics
2 answers:
Svet_ta [4.3K]15 days ago
4 0

Answer:

Her weekly expenses amount to $25.

Detailed reasoning:

Given: Jessica earns commissions for every sale but must cover her own spending costs.

She expresses her income function as E(x) = 7x - 25, where x represents the number of doors she approaches in a week and E(x) denotes her weekly earnings in dollars.

To determine: What are plausible meanings for the y-intercept in Jessica's earnings function?

Working it out:

E(x) = 7x - 25

x symbolizes the doors knocked per week

E(x) reflects her weekly total earnings in dollars.

Calculating the y-intercept:

Set x = 0

y= - 25

Given that E(x) is the net earning after expenses,

the value 25 corresponds to her weekly expenses.

Since she is responsible for covering costs,

if she makes zero sales, these expenses still apply.

Therefore, the y-intercept realistically represents her $25 weekly expenses.

PIT_PIT [3.9K]15 days ago
3 0

Answer:

The correct choice is D.

Step-by-step breakdown:

The provided equation is

E(x)=7x-25             .... (1)

where x stands for the weekly number of doors knocked, and E(x) is the weekly earnings in dollars.

The slope-intercept form of a linear equation is

y=mx+b           .... (2)

Comparing (1) and (2), we identify

m=7 and b=-25

The slope of 7 means she earns $7 per door knocked.

The y-intercept -25 (with the negative sign indicating costs) means she has $25 in weekly expenses.

Thus, the accurate interpretation is D.

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