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A plumber charges a [tex]$45 fee to make a house call and then $[/tex]25 for each hour of labor. The plumber uses an equation of the form [tex]y=mx+b[/tex] to determine the amount to charge each customer.

What is the value of [tex]m[/tex] in the equation?

[tex]m = [/tex] $

Sagot :

GinnyAnsweridn
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.
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