Question

Mike, a local auto mechanic charges a certain amount to diagnose and repair a car he bases his price on the amount of time that it takes for the repair.what is the equation for the passage above

Answer 1

From the graph given we have the following points:

Part 1 what's the equation

(0,50), (5,200)

We can find the slope in the following way:

`m=(y_2-y_1)/(x_2-x_1)=(200-50)/(5-0)=30`

Then we can find the intercept like this:

200 = 30(5) + b

b= 200-150 = 50

And the equation would be given by:

C= 30 x+ 50

Where x= time and C the cost

Part 2 process for 0 hours

30*0 +50

Part 3 total cost for zero hours

50

Part 4 process for 1 hours

30*1 +50

Part 5 total cost for 1 hours

80

Part 6 process for 2 hours

30*2 +50

Part 7 total cost for 2 hours

110

Part 8 process for 3 hours

30*3 + 50

Part 9 total cost for 3 hours

140

Part 10 process for 4 hours

30*4 + 50

Part 11 total cost for 4 hour

170

Part 12 process for 5 hours

30*5 +50

Part 13 total cost for 5 hours

200

Part 14 process for 6 hours

30*6+ 50

Part 15 total costs for 6 hours

230

Part 16 what is the rate of change of the graph and what does it represent what is the y-intercept of the graph and what does it represent what does the ordered pair (10, 350)

Rate of change = m =30

Y intercept = (0,50)

Part 17 represent in the context of the situation

Part 18 how much would it cost for a 9-hour repair

C= 30*9 +50 = 320

Part 19 if the cost of the repair was $470 how many hours did it take

470 = 30x+ 50

30x = 420

x= 420/30 =14

After 14 hours