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$.
