SOLUTION: Example: The table below displays data that relates the number of oil changes per year and the cost of engine repairs. Find the linear model for the data. Interpret the meaning

Question 1119689: Example:
The table below displays data that relates the number of oil changes per year and the cost of engine repairs. Find the linear model for the data. Interpret the meaning of the slope and y-intercept.

# of oil changes: Repair Costs in Dollars:
1 700
2 625
3 475
4 400
5 310
6 180
7 150
The first step is deciding which variable is the dependent variable. In this instance, the cost of repairs would depend on the number of oil changes (routinely getting oil changes would lessen the need for engine repairs). To get our linear model, we can choose two points, calculate the slope, and then find the equation. Let's choose the points (2, 625) and (6, 180).
m=180-625/6-2=-$111.25/oil change
y=mx+b
180=-111.25*6+b
847.5=b
y=-111.25x+847.5
Looking at the units on our slope, we see that our engine repair costs decrease by $111.25 with each additional oil change. The y-intercept is the value of our function at 0 or with no oil changes, so we would expect engine repair costs to be $847.50 if we didn't perform any routine oil changes on the vehicle.
Question:
Using the equation above, find the repair costs for 5 oil changes. Round to the nearest cent and leave off the $ symbol.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
y = -111.25x+847.5
Looking at the units on our slope, we see that our engine repair costs decrease by $111.25 with each additional oil change. The y-intercept is the value of our function at 0 or with no oil changes, so we would expect engine repair costs to be $847.50 if we didn't perform any routine oil changes on the vehicle.
Question:
Using the equation above, find the repair costs for 5 oil changes. Round to the nearest cent and leave off the $ symbol.
-----
f(5) = -111.25*5+847.5 = 291.25
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Cheers,
Stan H.
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