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
.
The linear equation to compute the total cost, y, for 1 month if x service calls are made is:
y = 5000 + 20x
The total cost y for x service calls can be calculated as follows:
y = $5000 (fixed monthly cost) + $20 (cost per service call) * x (number of service calls)
Therefore, the linear equation in slope-intercept form is:
y = 20x + 5000
To write the linear equation, we need to consider the fixed monthly cost of $5000 and the cost for each service call of $20.
The fixed monthly cost ($5000) is the y-intercept (b) in the equation because it is the cost even when no service calls are made.
The cost for each service call ($20) is the slope (m) in the equation because it represents the change in cost for every additional service call.
Therefore, the linear equation in slope-intercept form is:
y = mx + b
Replacing the slope (m) with the cost for each service call ($20) and the y-intercept (b) with the fixed monthly cost ($5000), we get:
y = 20x + 5000
This equation will allow us to compute the total cost (y) for 1 month if x service calls are made.