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)
