Question

Both of the following HVAC companies charge a service call fee and an hourly rate, for residential service.

For Richard's HVAC Service, a 6 hour service costs $195 and a 5 hour service costs $170

For Smith's HVAC Service, a 6 hour service costs $170 and a 5 hour service costs $152

For each company, find a linear model for the relationship between the hours spent on a repair and the total charges of a repair. Let,
x represent the number of hours of service and C represent the cost of the service

The linear model for Richard's HVAC Service:
C = ________

Answer 1

The linear model for Richard's HVAC Service is C = -25x + 345.

Step-by-step explanation:

To find the linear model for Richard's HVAC Service, we need to determine the equation that relates the number of hours spent on a repair (x) to the total cost of the service (C).

From the given information, we have the following:

For a 6 hour service: C = $195
For a 5 hour service: C = $170

To find the slope, we can subtract the two cost values and divide by the difference in hours:

Slope = (170 - 195) / (5 - 6) = $-25

To find the y-intercept, we can substitute the values of x and C from either of the given services in the equation and solve for the intercept:

195 = -25(6) + b

b = 195 + 150 = $345

Therefore, the linear model for Richard's HVAC Service is: C = -25x + 345.