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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]\$10[/tex].
B. For each additional door she knocks on, her earnings will increase by [tex]\$10[/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]\$35[/tex].

Sagot :

GinnyAnswer
Let's analyze the given function to understand what the slope represents.

Jessica's weekly earnings can be described by the linear function:
[tex]\[ E(x) = 10x - 35 \][/tex]
where:
- [tex]\( x \)[/tex] represents the number of doors she knocks on during the week.
- [tex]\( E(x) \)[/tex] represents her earnings for the week in dollars.

In a linear equation of the form [tex]\( y = mx + b \)[/tex], the coefficient [tex]\( m \)[/tex] represents the slope. The slope tells us how much the dependent variable [tex]\( y \)[/tex] changes for each unit increase in the independent variable [tex]\( x \)[/tex].

Here, the equation [tex]\( E(x) = 10x - 35 \)[/tex] has the slope [tex]\( m \)[/tex] equal to 10.

To understand what the slope represents in the context of Jessica's earnings:
- The slope is 10.
- This means that for each additional door she knocks on (one unit increase in [tex]\( x \)[/tex]), her earnings increase by \[tex]$10. Now, let's review the answer choices: A. For each additional set of books she sells, her earnings will increase by \$[/tex]10.
B. For each additional door she knocks on, her earnings will increase by \[tex]$10. C. For each additional set of books she sells, her earnings will increase by \$[/tex]35.
D. For each additional door she knocks on, her earnings will increase by \[tex]$35. The correct interpretation of the slope, based on the function \( E(x) \), is: - When the number of doors she knocks on increases by one, her earnings increase by \$[/tex]10.

Therefore, the correct answer is:
B. For each additional door she knocks on, her earnings will increase by \$10.
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