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) = 10x - 30, 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?

Check all that apply.

A. She will lose $10 per week if she does not knock on any doors.
B. Her expenses are $30 per week.
C. If she does not knock on any doors at all during the week, she will lose $30.
D. She can earn $10 per week even if she does not knock on any doors.

Answer 1

The correct option is B and C.

Explanation:

Consider the provided function.

`E(x) = 10x - 30`

Where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars.

We need to interpret the meaning of y-intercept.

Y-intercepts is a point where the value of x is zero.

Substitute the value of x = 0 in above function.

`E(x) = 10(0) - 30`

`E(x) =-30`

That means her expenses are 30 per week or if she doesn't knock on any doors, she would still have the expenses, therefore losing $30.

Her expenses are $30 and If she does not knock on any doors at all during the week, she will lose $30, So both A & B apply.

Hence, the correct option is B and C.