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)

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step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is