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)