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.

What does the slope of Jessica's function represent?

a. For each additional set of books she sells, her earnings will increase by $20.

b. For each additional door she knocks on, her earnings will increase by $20.

c. For each additional set of books she sells, her earnings will increase by $50.

d. For each additional door she knocks on, her earnings will increase by $50.

Answer 1

Hello there.

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.


b. For each additional door she knocks on, her earnings will increase by $20.

Answer 2

For the answer to the question above, 
since the only variable used to determine earnings is the number of doors knocked, you can eliminate options 1 and 3 as they are based on the number of books sold, which is not a part of the equation. 

That leaves the only options being the increase of $20 or $50 for each door knocked. As the x value we multiply by 20, the correct answer is #2, her earnings will increase by $20 for each door knocked. 

You can also check this by plugging in values: 

Assume 10 doors are knocked: 
E(10) = 20(10)-50 = 200-50 = 150 

Assume 11 doors (1 more door) is knocked: 
E(11) = 20(11)-50 = 220-50 = 170 

The increase from 1 door is $20.