3. LINEAR MODELS
23
Determining if a data set is directly proportional
Example. This is Example 2 from page 30 redone with di↵erent data –
buying gas at the pump.
Gallons
Cost
3.50
10.15
6.28
18.21
17.34
50.28
We check to see if this relationship is directly proportional:
10.15
18.21
50.28
= 2.9,
= 2.89968,
= 2.89965
3.50
6.28
17.34
As given, the data is not directly proportional since the ratios are not equal,
although they are very close.
But experience tells us that the cost of gas is directly proportional to the amount
purchased. The issue is that gas is priced to the tenth of a cent.
From our data, suppose we use the directly proportional model y = 2.899x.
x=Gallons
Cost y = cost by model estimate
3.50
10.15 10.14965
6.28
18.21 18.211372
17.34
50.28 50.284266
The cost you pay is the cost from the model rounded to the nearest cent. ⇤