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.
