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: [tex]E(x)=10x-35[/tex], where [tex]x[/tex] is the number of doors she knocks on during the week and [tex]E(x)[/tex] 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 [tex]\$10[/tex].
B. For each additional door she knocks on, her earnings will increase by [tex]\$35[/tex].
C. For each additional set of books she sells, her earnings will increase by [tex]\$35[/tex].
D. For each additional door she knocks on, her earnings will increase by [tex]\$10[/tex].

Question

09-07-2024
Mathematics

Answered

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: [tex]E(x)=10x-35[/tex], where [tex]x[/tex] is the number of doors she knocks on during the week and [tex]E(x)[/tex] 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 [tex]\$10[/tex].
B. For each additional door she knocks on, her earnings will increase by [tex]\$35[/tex].
C. For each additional set of books she sells, her earnings will increase by [tex]\$35[/tex].
D. For each additional door she knocks on, her earnings will increase by [tex]\$10[/tex].

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-09T13:07:31-04:00

To understand what the slope of Jessica's function represents, we first need to interpret the given equation:

[tex]\[ E(x) = 10x - 35 \][/tex]

Here, [tex]$ E(x) $[/tex] is Jessica's earnings for the week in dollars, and [tex]$ x $[/tex] is the number of doors she knocks on during the week.

The equation [tex]$ E(x) = 10x - 35 $[/tex] is written in the slope-intercept form, [tex]$ y = mx + b $[/tex], where [tex]$ m $[/tex] represents the slope and [tex]$ b $[/tex] represents the y-intercept.

In this equation:

- The coefficient of [tex]$ x $[/tex], which is 10, is the slope.
- The constant term, which is -35, is the y-intercept.

The slope of a linear function represents the rate of change of the dependent variable (Jessica's earnings) per unit change in the independent variable (the number of doors she knocks on).

So, in Jessica's case, the slope (10) tells us how much her weekly earnings will change for each additional door she knocks on. A slope of 10 means that for every extra door she knocks on, her earnings increase by [tex]$10. Therefore, the correct interpretation of the slope in this context is: D. For each additional door she knocks on, her earnings will increase by $[/tex]10.