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The table below shows that the number of miles driven by Ellie is directly proportional to the number of...

The table below shows that the number of miles driven by Ellie is directly proportional to the number of gallons she used.
| Gallons Used | Miles Driven |
|--------------|--------------|
| 33 | 1359.6 |
| 43 | 1771.6 |
| 50 | 2060 |
If m represents the number of miles driven for any number of gallons used, g, write a proportional equation for m in terms of g that matches the context.

Answer

To find the proportional equation, we need to determine the constant of proportionality, k. This can be found by dividing the miles driven by the gallons used for any of the data points.

  1. For 33 gallons: k = 1359.6 / 33 = 41.2
  2. For 43 gallons: k = 1771.6 / 43 = 41.2
  3. For 50 gallons: k = 2060 / 50 = 41.2

Since k is consistent, the proportional equation is:

m = 41.2g

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