Meteorologists often measure the intensity of a tropical storm or hurricane by the maximum sustained wind speed and the minimum pressure. The relationship between these two quantities is approximately linear. Hurricane A had a maximum sustained wind speed of

Question

150
knots and a minimum pressure of
873

mb
(millibars). Hurricane B had maximum sustained winds of
76
knots and a pressure of
564

mb
.
(b) Using the slope found in part (a) and the point
76, 564
, find a linear model that represents the minimum pressure of a hurricane,
y
, versus its maximum sustained wind speed,
x
.

Answer 1

To find the linear model that represents the minimum pressure of a hurricane (y) versus its maximum sustained wind speed (x), we need to use the slope found in part (a) and the point (76, 564).

The slope found in part (a) is the change in pressure (y) divided by the change in wind speed (x). Let's denote the slope as m.

m = (873 - 564) / (150 - 76) = 309 / 74 ≈ 4.1757

Using the point-slope form of a linear equation, we can write the linear model as:

y - 564 = 4.1757(x - 76)

Simplifying,

y - 564 = 4.1757x - 318.3052

Moving the constant term to the other side,

y = 4.1757x - 318.3052 + 564

y = 4.1757x + 245.6948

So, the linear model that represents the minimum pressure of a hurricane (y) versus its maximum sustained wind speed (x) is:

y = 4.1757x + 245.6948