To understand what the slope of Jessica's function represents, we need to analyze the given equation of her weekly earnings: [tex]\(E(x) = 10x - 35\)[/tex].
In the equation [tex]\(E(x) = 10x - 35\)[/tex]:
- [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 number 10 is the coefficient of [tex]\(x\)[/tex], which is the slope of the linear function.
- The number -35 is the y-intercept, which does not affect the slope but shifts the line up or down.
The slope of a linear function [tex]\(y = mx + b\)[/tex] is the coefficient [tex]\(m\)[/tex], which represents the rate of change of [tex]\(y\)[/tex] with respect to [tex]\(x\)[/tex]. In our specific equation:
- The slope [tex]\(m\)[/tex] is 10.
This tells us how much [tex]\(E(x)\)[/tex] (Jessica's earnings) changes for each unit increase in [tex]\(x\)[/tex] (the number of doors she knocks on).
Specifically, a slope of 10 means that for every additional door Jessica knocks on, her earnings increase by [tex]$10.
Thus, the correct interpretation of the slope in this context is captured by option:
B. For each additional door she knocks on, her earnings will increase by \$[/tex]10.
