When measuring the wind speed of a hurricane or similar storm, meteorologists don't want to get hit by flying debris. They use a measure available to them in the comfort of their TV studio. Luckily for the meteorologists, the barometric pressure is linearly related to the wind speed. Suppose scientists compared the wind speeds and barometric pressure readings of two severe storms over the Atlantic Ocean. For one of the storms, the barometric pressure was 1,000 mb (millibars), and the maximum wind speed was 100 kmh (kilometers per hour). The second had a barometric pressure of 960 mb and maximum wind speeds of 180 kmh.

a) develop a rule that you could use to predict the wind speed given any barometric pressure
b) use your rule to predict the wind speed of a hurricane with a barometric pressure of 980 mb. using what you know about linearity, explain why your prediction is reasonable
c) interpret the intercept for wind speed in this context (i.e., as it pertains to the weather)
d) explain the meaning of slope in this context

Solution

a) Since the relationship is linear, we'll build a formula using the two points

(1000, 100) and (960, 180)

Slope-intercept form

y = mx + b

Finding the slope and y-intercept:

m = (180-100)/(960 - 1000) = 80/-40 = -2
100 = -2*1000 + b ⇒ b = 2100

So the function is

y = -2x + 2100

b) x = 980

Using the function to find the wind speed:

y = -2*980 + 2100 = 140 kmh

c) y-intercept is acting as correlation to barometric pressure demonstrating absolute wind speed in case zero barometric pressure (impossible in natural condition)

d) Negative slope demonstrates decreasing wind speed as barometric pressure increases