The rate a plumber charges is described by the function y = 21x + 45,

Question

where x is the number of hours worked and y is the total charge
The real-world meaning of the y-coordinate of the y-intercept is?

Answer 1

In the equation \( y = 21x + 45 \), the y-coordinate of the y-intercept occurs when \( x = 0 \). At this point, the equation simplifies to:

\[ y = 21(0) + 45 = 45 \]

Thus, the y-intercept is \( (0, 45) \).

In the context of the problem, where \( y \) represents the total charge and \( x \) represents the number of hours worked, the y-intercept value of 45 represents the base charge or fee that the plumber charges for service, regardless of the number of hours worked. This means that if no hours are worked (i.e., the plumber is contacted but no time is spent on the job), the total charge will still be $45. Thus, the real-world meaning of the y-coordinate of the y-intercept is the initial fee or the minimum charge for the plumber's service.