Question

The cost for a mechanic increases linearly as the number of hours needed to fix a car increases. A mechanic worked 5 hours and charged $375. The same mechanic worked 12 hours and charges $795.

A) write a equation that describes the relationship.
B) what does the slope mean in terms of the context?
C) what is the y-intercept? What does it mean in terms of the context.
D) how much would someone be charged if the mechanic spent 3 hours fixing her car?

Answer 1

The labor cost equation is y = 55x + 75. The slope indicates the rate of cost increase per hour, and the y-intercept represents the flat fee. If the mechanic spends 3 hours on a car, the charge would be $240.

Correct option is A

Step-by-step explanation:

The independent variable in this situation is the number of hours worked on a car, while the dependent variable is the total labor charges to fix the car.

The equation that describes the relationship is y = 55x + 75, where y represents the total charge and x represents the number of hours required.

The slope of the equation, which is 55, represents the rate at which the labor cost increases per hour. In this context, it means that for every additional hour worked, the labor cost increases by $55.

The y-intercept of the equation, which is 75, represents the total cost when no hours are worked. In terms of the context, it means that there is a flat fee of $75 charged regardless of the number of hours worked.

If the mechanic spent 3 hours fixing a car, the equation can be used to find the labor charge. Substituting x = 3 into the equation: y = 55(3) + 75 = 165 + 75 = $240.