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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][tex]$E(x)$[/tex][/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]$\[tex]$10$[/tex][/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]$\[tex]$35$[/tex][/tex].



Answer :

GinnyAnswer
To understand what the slope of Jessica's function represents, let's break down the linear function provided:

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

In this equation:
- [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 general form of a linear equation is:

[tex]\[ E(x) = mx + b \][/tex]

where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept.

In Jessica's equation:
- The slope [tex]\( m \)[/tex] is 10.
- The y-intercept [tex]\( b \)[/tex] is -35.

The slope of a linear function tells us how much the dependent variable (in this case, Jessica's earnings) changes for every one-unit increase in the independent variable (in this case, the number of doors knocked on).

Since the slope [tex]\( m \)[/tex] is 10, this means:

- For every additional door Jessica knocks on, her earnings increase by [tex]$10. Therefore, the correct interpretation of the slope in Jessica's function is: B. For each additional door she knocks on, her earnings will increase by $[/tex]10.