To determine the slope of the cost function for Shannon's new clothing store, let's first understand the structure of the given function. The cost function is:
[tex]\[ C = 8.75n + 925 \][/tex]
This is a linear function of the form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( y \)[/tex] (or [tex]\( C \)[/tex] in this specific case) is the dependent variable (cost).
- [tex]\( x \)[/tex] (or [tex]\( n \)[/tex] in this specific case) is the independent variable (number of T-shirts sold).
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept, which represents the fixed cost when no T-shirts are sold.
To identify the slope in a linear function [tex]\( y = mx + b \)[/tex], we look at the coefficient of the independent variable [tex]\( x \)[/tex].
For the given cost function:
[tex]\[ C = 8.75n + 925 \][/tex]
The coefficient of [tex]\( n \)[/tex] (which represents the number of T-shirts sold) is [tex]\( 8.75 \)[/tex].
Thus, the slope of the cost function is:
[tex]\[ \boxed{8.75} \][/tex]
Therefore, the correct answer is:
D. \$ 8.75
