Bob recently damaged his electric guitar. he went to a guitar store and asked the owner of the store how much would it cost him to repair his guitar. the owner of the guitar shop charges the labor rates shown for electric guitar repairs. what linear function can bob use to determine the cost of a repair that takes 5.5 hours and includes $180 in parts?

You need to come up with the linear equation that fits the data in the table.
I notice immediately that if we move from 1 hour to 2 hours, the labor charge doubles from $85 to $170.

In other words, as we go from (1,$85) to (2,$170), x increases by 1 and y (labor charge) increases by $85 to $170 (which is double $85).

What is the slope of this line?  
        
        rise       $85
m = = = $85/ hour.  The shop charges $85 per hour for labor.
         run        2-1

We still have to find the y-intercept.  Let's use the slope-intercept form:

y = mx + b.  Here let's sub. 170 for y, 85 for m, 2 for x, and solve for b:

170=85(2)+b, or 170 = 170+b.  Seems as tho' b = 0!

Thus, the equation of this str. line is just y = $85x.

We have to create a linear function that Bob can use to determine the cost of repairs if the repair takes 5.5 hours and includes $180 in parts:

Total cost = C(x) = (cost of parts) + (labor cost)
                           =            P          +         y            (where y = $85x, from      
                                                                                above)

Here, if the parts cost $180 and the repair took 5.5 hours, the total cost C(5.5) would be:

C(5.5) = $180 + ($85/hr)(5.5 hr) = $647.50              (answer)