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The temperature at which water starts to boil is called its boiling point and is linearly related to the...

The temperature at which water starts to boil is called its boiling point and is linearly related to the altitude. Water boils at 212°F at sea level and at 193.6°F at an altitude of 10,000 feet.
(a) Find a relationship of the form T = mx + b, where T is degrees Fahrenheit and x is altitude in thousands of feet.
(b) Find the boiling point at an altitude of 4,500 feet.
(c) Find the altitude if the boiling point is 198.5°F.
(d) Graph T and illustrate the answers to (b) and (c) on the graph.
(d) Graph T: Choose the correct graph below.

Answer

  1. (a) To find the relationship T = mx + b, we use the points (0, 212) and (10, 193.6). The slope m is calculated as:
    m = (193.6 - 212) / (10 - 0) = -1.84.
    Using the point (0, 212), the equation becomes:
    T = -1.84x + 212.

  2. (b) For an altitude of 4,500 feet (x = 4.5):
    T = -1.84(4.5) + 212 = 203.72°F.

  3. (c) To find the altitude when T = 198.5°F:
    198.5 = -1.84x + 212
    x = (212 - 198.5) / 1.84 = 7.35 (thousands of feet) = 7,350 feet.

  4. (d) The correct graph is the one that shows a line with a slope of -1.84, passing through the points (0, 212) and (10, 193.6), and includes the points (4.5, 203.72) and (7.35, 198.5).

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