Apex Plumbing charges a trip fee of $55 plus $15 for each quarter hour of service. John wrote an equation using, t , the total cost of a service call, as a function of, h , the number of hours the call lasted. What is the value of the slope in his equation and what does it represent?
Slope 15
The equation for the total cost, t, as a function of the number of hours, h, can be written as:
t = 55 + 15h
In this equation, the coefficient of h, which is 15, represents the slope. The slope represents the rate at which the cost of the service call increases for each additional hour of service. In this case, it means that for every additional hour of service, the cost increases by $15.
To find the value of the slope in John's equation, let's break down the given information.
According to the information provided:
- Apex Plumbing charges a trip fee of $55. This is a fixed cost, regardless of the duration of the service call.
- Additionally, they charge $15 for each quarter hour of service. This is a variable cost that depends on the number of quarter hours, or 15-minute intervals, that the service call lasted.
Now, let's set up an equation using this information:
Total Cost (t) = Fixed Cost (trip fee) + Variable Cost (cost per quarter hour * number of quarter hours)
We know that the trip fee is $55, and the variable cost is $15 per quarter hour. Let's represent the number of quarter hours as (4 * h), as each hour contains 4 quarter hours.
So the equation becomes:
t = 55 + 15 * (4 * h)
To find the slope in this equation, we need to express it in slope-intercept form, y = mx + b, where y represents the total cost (t), and x represents the number of hours (h).
Rearranging the equation, we have:
t = 55 + 15 * (4 * h)
t = 55 + 60h
Comparing this to the slope-intercept form, we can conclude that the slope (m) is 60. The slope represents the rate at which the total cost increases as the number of hours increases.
Therefore, in this case, the slope of 60 means that for every additional hour, the cost of the service call increases by $60.
dI hope John wrote
t = 60h + 55
the slope is 60 and it represents the hourly rate of $60
($15 per quarter hour = $60/hr)