For every room added, the price increase is $50, therefore the slope is equal to 50.
Since the value for one room is $125 and we know that each room costs $50, then the y-intercept is the value for 1 room minus 50.
[tex]b=125-50=75[/tex]
Now we can create the function for this situation:
[tex]f(x)=50\cdot x+75[/tex]
Where f(x) is the price and x is the number of rooms to be cleaned. Since the function is linear, the unit rate is equal to the slope, so the unit rate is 50.
The amount charged to drive to the client's home is the fixed part of the price, so it is equal to the y-intercept. The price is $75.
To find the cost of 8 rooms we need to make x = 8 and calculate the value of the expression.
[tex]f(8)=50\cdot8+75=475[/tex]
The value would be $475.
