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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)=20x-50[/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 door she knocks on, her earnings will increase by \[tex]$20.
B. For each additional set of books she sells, her earnings will increase by \$[/tex]20.
C. For each additional set of books she sells, her earnings will increase by \[tex]$50.
D. For each additional door she knocks on, her earnings will increase by \$[/tex]50.

Sagot :

GinnyAnswer
To determine the interpretation of the slope in Jessica's earnings function [tex]\( E(x) = 20x - 50 \)[/tex], we first need to understand the components of a linear equation of the form [tex]\( E(x) = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

In Jessica's function:

- [tex]\( E(x) \)[/tex] represents her earnings for the week in dollars.
- [tex]\( x \)[/tex] represents the number of doors she knocks on during the week.
- The slope [tex]\( m = 20 \)[/tex] represents the rate of change in her earnings with respect to the number of doors knocked on.
- The y-intercept [tex]\( b = -50 \)[/tex] represents her fixed expenses.

The slope [tex]\( m = 20 \)[/tex] means that for each additional door Jessica knocks on, her earnings increase by [tex]$20. Now, let's look at the given choices: A. For each additional door she knocks on, her earnings will increase by $[/tex]\[tex]$ 20$[/tex].
B. For each additional set of books she sells, her earnings will increase by [tex]$\$[/tex] 20[tex]$. C. For each additional set of books she sells, her earnings will increase by $[/tex]\[tex]$ 50$[/tex].
D. For each additional door she knocks on, her earnings will increase by [tex]$\$[/tex] 50[tex]$. Given that the slope \( m = 20 \), the correct interpretation is that for each additional door Jessica knocks on, her earnings will increase by $[/tex]20. Therefore, the correct answer is:

A. For each additional door she knocks on, her earnings will increase by [tex]$\$[/tex] 20$.
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