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) = 7x - 25[/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]$\$[/tex]7[tex]$.
B. For each additional set of books she sells, her earnings will increase by $[/tex]\[tex]$25$[/tex].
C. For each additional set of books she sells, her earnings will increase by [tex]$\$[/tex]7[tex]$.
D. For each additional door she knocks on, her earnings will increase by $[/tex]\[tex]$25$[/tex].



Answer :

GinnyAnswer
To understand what the slope of Jessica's function represents, let's carefully analyze the given function and its components.

The function provided is:
[tex]\[ E(x) = 7x - 25 \][/tex]
where [tex]\( E(x) \)[/tex] represents her weekly earnings in dollars, and [tex]\( x \)[/tex] is the number of doors she knocks on during the week.

This is a linear function of the form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept.

In the given function:
- The slope ([tex]\( m \)[/tex]) is 7.
- The y-intercept ([tex]\( b \)[/tex]) is -25.

The slope of a linear function tells us how much the dependent variable (in this case, her earnings [tex]\( E(x) \)[/tex]) changes for a one-unit increase in the independent variable (in this case, the number of doors [tex]\( x \)[/tex]).

Thus, the slope of 7 indicates that for each additional door Jessica knocks on, her earnings will increase by [tex]$7. Therefore, the correct interpretation of the slope is: A. For each additional door she knocks on, her earnings will increase by $[/tex]\[tex]$ 7$[/tex].