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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]$\$[/tex] 10[tex]$.
B. For each additional door she knocks on, her earnings will increase by $[/tex]\[tex]$ 10$[/tex].
C. For each additional door she knocks on, her earnings will increase by [tex]$\$[/tex] 35[tex]$.
D. For each additional set of books she sells, her earnings will increase by $[/tex]\[tex]$ 35$[/tex].

Sagot :

GinnyAnsweridn
To understand what the slope of Jessica's function represents, we need to analyze the given equation of her weekly earnings: [tex]\(E(x) = 10x - 35\)[/tex].

In the equation [tex]\(E(x) = 10x - 35\)[/tex]:

- [tex]\(E(x)\)[/tex] represents Jessica's earnings for the week in dollars.
- [tex]\(x\)[/tex] represents the number of doors she knocks on during the week.
- The number 10 is the coefficient of [tex]\(x\)[/tex], which is the slope of the linear function.
- The number -35 is the y-intercept, which does not affect the slope but shifts the line up or down.

The slope of a linear function [tex]\(y = mx + b\)[/tex] is the coefficient [tex]\(m\)[/tex], which represents the rate of change of [tex]\(y\)[/tex] with respect to [tex]\(x\)[/tex]. In our specific equation:
- The slope [tex]\(m\)[/tex] is 10.

This tells us how much [tex]\(E(x)\)[/tex] (Jessica's earnings) changes for each unit increase in [tex]\(x\)[/tex] (the number of doors she knocks on).

Specifically, a slope of 10 means that for every additional door Jessica knocks on, her earnings increase by [tex]$10. Thus, the correct interpretation of the slope in this context is captured by option: B. For each additional door she knocks on, her earnings will increase by \$[/tex]10.
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