8. some carpet cleaning costs are shown in the table. the relationship is linear. find and interpret the rate of change and the initial value for this situation ( i need in all the page)

8)
first calculate the hourly rate, which is the difference of cleaning 2 and 1 rooms:
175-125=50

then calculate the initial value by subtracting the hourly rate from the "1 room" cost:
125-50=75

The initial cost might be something like driving to the place (which is only necessary once), while the rate covers work time or cleaning utensils used.

9)
a)
first calculate the hourly rate, which is the difference of the second and first hour:
29-17=12
then calculate the value at "0" hours, so the parking cost by subtracting the hourly cost from the first hour value:
17-12=5
-> f(h)=12h+5
b)
insert time h=3.5
12*3.5+5
36+6+5=47

or alternatively add the half hour to the value of 3:
41+(12/2)=41+6=47

then because they split the cost divide it by 2:
47/2=23.5

10)to calculate the rate of change again subtract the 1 hour lesson cost from the 2 hour cost
rate of change (group):85-55=30
rate of change (private):125-75=50

then subtract the rate of change from the first value to get the initial value:
initial (group):55-30=25
initial (private):75-50=25

so both types of lessons share their initial cost, but the hourly rate is nearly double for private lessons compared to group ones.

4-2/3--2=

4-2/3+2=

2/5

the slope is 2/5