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.
