If a 8 hour repair costs $570 and a 7 hour repair costs $510, find a linear model for the relationship between the hours spent on a repair and the total charges of a repair.

 The linear function   y = 60x + 90  can be used  to model the relationship between the hours and costs of a repair.

Step-by-step explanation:

In this model or function we will represent the number of hours by x and the cost by y.

Using that information we can generate two points ,  (8, 570)  and (7,510)  

Now to write a linear function we will need to find the slope which will be the cost per hour, and the y intercept which will be the initial amount .

To find the slope we will find the difference in the y coordinates of the points and divide it by the difference in the x coordinates.

570 - 510 = 60

8 - 7 =  1  

Slope:  60 / 1 = 60  

We will have to find the y intercept by using the formula  y = mx + b.

We will input the x and y coordinates of a given point plus the slope into the formula to solve for b.

570 = 60(8) + b

570 = 480 + b

-480   -480  

  b =  90    

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step-by-step explanation:

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