Tariq is a mechanic. He charges his customers by the hour. The first hour of service costs $122. The second hour of service costs $171.99. The third hour of service costs $221.98. Write an equation in the form of
y=c+d(x−1)
to represent this situation. Explain how you got your equation.

y = $122 + $49.99(x - 1)

Step-by-step explanation:

Let's use the general equation y=c+d(x−1), where c represents the initial charge and x represents the specific hour:  {1, 2, 3}.

Then:

First hour:  $122 = c + d(1 - 1) = c

If c = $122, then:

Second hour:  $171.99 = $122 + d(2 - 1), or $49.99 + d(1), so that d = $49.99.

Third hour:  $221.98 = $122 + $49.99(3 - 1), or

                         $99.98 = $99.98

Thus, the governing equation becomes

y = $122 + $49.99(x - 1)

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80