Certainly! Let's break down how to determine the value of [tex]\( m \)[/tex] in the equation [tex]\( y = mx + b \)[/tex] for the plumber's charges.
- The equation [tex]\( y = mx + b \)[/tex] represents a linear relationship where:
- [tex]\( y \)[/tex] is the total amount charged.
- [tex]\( m \)[/tex] is the slope or the rate at which the cost increases per hour of labor.
- [tex]\( x \)[/tex] is the number of hours of labor.
- [tex]\( b \)[/tex] is a constant, representing the initial charge or fee.
Given the information:
- The plumber charges a [tex]$45 fee just to make a house call. This corresponds to the constant term \( b \).
- The plumber then charges $[/tex]25 for each hour of labor. This per-hour rate corresponds to the coefficient [tex]\( m \)[/tex].
So, in the equation [tex]\( y = mx + b \)[/tex]:
- [tex]\( m \)[/tex] is the charge per hour, which is clearly stated as [tex]$25.
Thus, the value of \( m \) is:
\[ m = 25 \]
So, the slope or rate \( m \) in the equation \( y = mx + b \) is \$[/tex]25.
