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One carpet cleaning cost are shown in the table. The relationship is linear. Find and interpret the rate of change and the initial value for this situation.

One carpet cleaning cost are shown in the table The relationship is linear Find and interpret the rate of change and the initial value for this situation class=

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I see from the given data that each additional carpet after the first costs $50 each to have cleaned.

The first costs $125.  Supposing we subtract $50 from that, we get $75.  So, it sounds like it costs $75 just to get the carpet cleaners to your house.

The rule would then be $75 + $50x, where x : {1, 2, 3, 4, .... }

Let's check this result.  Suppose x = 1.  Will the charge be $125, as show in the table?  $75 + $50(1) = $125.  Correct.

Suppose x = 4.  Will the charge be $275 as shown in the table?
   $75 + $50(4) = $275.  YES
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