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.
