There is a close relationship between the air pressure inside a hurricane and its maximum sustained wind speed: [tex]y = -1.22x + 1250[/tex] where [tex]x[/tex] is the air pressure in millibars (kPa) and [tex]y[/tex] is the wind speed in knots (nautical miles per hour).

What does the slope of the line represent?

A. the wind speed of a hurricane with an air pressure of 0 kPa
B. the change in wind speed for every hour
C. the change in wind speed for every 1 kPa increase in air pressure
D. the wind speed of a hurricane with an air pressure of 1000 kPa



Answer :

To understand what the slope of the line represents in the given equation, let's analyze the given linear relationship:

[tex]\[ y = -1.22x + 1250 \][/tex]

Where:
- [tex]\( x \)[/tex] is the air pressure in kilopascals (kPa),
- [tex]\( y \)[/tex] is the wind speed in knots.

The general form of a linear equation is:

[tex]\[ y = mx + b \][/tex]

Where:
- [tex]\( m \)[/tex] is the slope of the line,
- [tex]\( b \)[/tex] is the y-intercept.

In the provided equation, we can identify that the slope [tex]\( m \)[/tex] is [tex]\(-1.22\)[/tex].

The slope of a line in such a relationship represents the rate at which the dependent variable [tex]\( y \)[/tex] changes with respect to the independent variable [tex]\( x \)[/tex]. Specifically, in this context:

- The slope [tex]\( -1.22 \)[/tex] tells us how much the wind speed ( [tex]\( y \)[/tex] ) changes for each unit increase in air pressure ( [tex]\( x \)[/tex] ).

To interpret this meaning clearly:

1. A positive slope would indicate that as air pressure increases, the wind speed would also increase.
2. A negative slope (as in this equation, which is [tex]\(-1.22\)[/tex]) indicates that as the air pressure increases, the wind speed decreases.

Thus, for each 1 kPa (kilopascal) increase in air pressure, the wind speed decreases by 1.22 knots.

Therefore, the correct interpretation of the slope is:

C. the change in wind speed for every 1 kPa increase in air pressure.