An air-conditioning and heating company has a fixed monthly cost of
$5000
. Furthermore, each service call costs the company
$20
.
(a) Write a linear equation to compute the total cost,
y
, for
1
month if
x
service calls are made.
The linear equation in slope-intercept form is
.
y = 20x + 5000
To write a linear equation in slope-intercept form, we need to determine the slope and y-intercept.
We know that the fixed monthly cost is $5000, which represents the y-intercept. This means that even if the company doesn't make any service calls, they still have to pay $5000.
Each service call costs the company $20. This represents the slope of the linear equation. The cost increases by $20 for each service call made.
So, the linear equation to compute the total cost, y, for x service calls can be written as:
y = 20x + 5000
The linear equation in slope-intercept form is y = mx + b, where y represents the total cost, x represents the number of service calls, m represents the cost per service call, and b represents the fixed monthly cost.
In this case, the cost per service call is $20 and the fixed monthly cost is $5000. Therefore, the linear equation is:
y = 20x + 5000