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 of Jessica's function?

Check all that apply:
1. She can earn $10 per week even if she does not knock on any doors
2. She will lose $10 per week if she does not knock on any doors
3. Her expenses are $30 per week
4. If she does not knock on any doors at all during the week, she will loose $30

For any equation where a variable is apart of a term in the equation, it can be considered a function. (I.e. [tex]2x^2+4x+7[/tex], 3x+124, etc.)

A function takes in an "input" value or x-value that's substituted into all the variable part(s) and is evaluated to find the y-value or "output" value of the function/equation.

Y - Intercepts

The constant value of a function or equation is always the y-intercept or, the y - value when x=0 is plugged into the function/equation.

Solving the Problem

Solution: Y - Intercepts

Looking at E(x) we can deduce that -30 is the y-intercept value. This can be verified by plugging x = 0:

E(0) = 10(0) - 30 = 0 - 30 = -30.

Knowing that for x = 0, y = -30 we know that answer choice 4 is correct and that choices 1 and 2 are not.

Rereading the word problem we know that Jessica's must pay for her expenses using her commission money she gains by selling books to various houses.

Knowing that the value of x is in terms for one week, her weekly commission money can be seen in the "10x" term of E(x), leaving that "-30" to be her weekly expenses. Thus, answer choice 3 is also correct.