Final answer:
The relationship between altitude and boiling point of a liquid is linear. The equation giving the boiling point b of the liquid in terms of altitude a is b = -0.0152a + 326.8. At an altitude of 2500 feet, the boiling point of the liquid is 204.8°F.
Step-by-step explanation:
The relationship between altitude and boiling point of a liquid is linear. In this case, we can use the equation of a line, y = mx + b, where y is the boiling point in degrees Fahrenheit, x is the altitude in feet, and m and b are constants. To find the equation, we can use the given data points: (8000, 202.4) and (4700, 206.36).
First, we need to find the slope, m, which is (change in y) / (change in x). m = (202.4 - 206.36) / (8000 - 4700) = -0.0152.
Next, we can use one of the data points and the slope to find the y-intercept, b, in the equation y = mx + b. Using (8000, 202.4), we get 202.4 = -0.0152 * 8000 + b. Simplifying, we find b = 326.8.
Therefore, the equation giving the boiling point b of the liquid in terms of altitude a is b = -0.0152a + 326.8. To find the boiling point at 2500 feet, we substitute a = 2500 into the equation: b = -0.0152 * 2500 + 326.8 = 204.8°F.