trying to solve a point a slope word problem.

you are scheduled to start your job at an oil change shop 2 hours after shop opens. two hours after you start, a total of 11 cars have had their oil changed. three hours later, a total of 14 cars have had their oil changed. At what rate are cars getting their oil changed since you started working? How many cars had theri oil changed before you started work?

would I set up as 14-11/3-2=changes?

It is not clear to me what you mean by

"Three hours later"
Is it three hours after he started working or is it five hours after you start
According to the work you show, you assumed it is 3 hours after you start.

Once you have established that, yes, take the slope
then find the equation, just like you would for 2 points on a straight line. Finally find the "y-intercept", when t = 0

To solve this point-slope word problem, we need to first understand how to calculate the rate of change, or slope.

The rate of change, or slope, represents how the number of cars getting their oil changed is changing over time. In this case, we need to calculate the rate at which cars are being serviced since you started working.

Let's break down the problem:

Step 1: Calculate the rate of change
To find the rate, we will use the formula:

Rate of Change = (Change in Number of Cars) / (Change in Time)

From the problem, it is given that two hours after the shop opens, 11 cars have had their oil changed, and three hours later (after you start working), the total becomes 14 cars. Therefore:

Change in Number of Cars = 14 - 11 = 3
Change in Time = 3 - 2 = 1

Now we can calculate the rate of change:

Rate of Change = 3/1 = 3 cars per hour

So, the rate at which cars are being serviced since you started working is 3 cars per hour.

Step 2: Calculate the number of cars that had their oil changed before you started work
To find the number of cars that had their oil changed before you started work, we need to calculate the total number of cars serviced in the two hours before your start time.

Given that two hours after the shop opens, 11 cars have had their oil changed, and you started work two hours later:

Total Number of Cars Serviced Before You Started = 11 cars

Therefore, the number of cars that had their oil changed before you started work is 11.

In conclusion, the rate at which cars are getting their oil changed since you started working is 3 cars per hour, and the number of cars that had their oil changed before you started work is 11.