Question

Water boils at 212 degrees F at sea level (altitude 0 ft), 204.6 degrees F at 40000 ft, 197.2 deg. F at 8000 ft, and 189.8 deg. F at 12,000 ft. Find a good model relating the boiling temperature t of water to the altitude a.Is the model linear or quadratic?

Answer 1

0 ft altitude to 4,000 ft (I assume you made a typo) is an increase of 4,000 ft and a decrease of 7.4 degrees F.

4,000 ft to 8,000 ft is an increase of 4,000 ft and a decrease of 7.4 degrees.

8,000 ft to 12,000 ft is an increase of 4,000 ft and a decrease of 7.4 degrees.

So, from the data given, the trend is that each increase in 4,000 ft altitude results in a drop of 7.4 degrees F.

Let y = degrees F and x = altitude in ft. Then y = 212 - 7.4(x / 4000)

Which can be reexpressed as:
y = 212 - 7.4x / 4000
or
y = 212 - (7.4/4000)x
or
y = (-7.4/4000)x + 212
or
y = (-74/40000)x + 212
or finally
y = (-37/20000)x + 212

There's you functional model

Now, does that look like it fits the equation of a line, y = mx + b???