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].
