Question

Atmospheric pressure is caused by the weight of the air in Earth's atmosphere. Atmospherie pressure is measured in millibars. Changes in weather often cause changes in atmospheric pressure. In addition to monitoring the wind speed of the hurricane, researchers monitor the atmospheric pressure inside the storm. The measures are recorded in the table. Time, x (hours) 18 36 84 Atmospheric pressure, y (millibars) 1008 999 975 6. Use the data from the table to write a linear equation that models the change in atmospheric pressure over time.​

Answer 1

The linear equation that models the change in atmospheric pressure over time is y=− 1/2 x+1017

To write a linear equation that models the change in atmospheric pressure over time, we can use the slope-intercept form of a linear equation, which is given by:

y=mx+b

where:

y is the dependent variable (atmospheric pressure),

x is the independent variable (time),

m is the slope of the line,

b is the y-intercept (the atmospheric pressure when time is 0).

To find the slope (m), we can use the formula

m= Δy/Δx

where

Δy is the change in atmospheric pressure and

Δx is the change in time.

Using the data from the table:

m= 975−188/84−18​ =−33 /66​=− 1/2

​Now, we need to find the y-intercept (b). We can choose any point from the table to substitute into the equation. Let's use the point (18, 1008):

1008=− 1/2 (18)+b

Now, solve for b:

b=1008+9=1017

So, the linear equation that models the change in atmospheric pressure over time is:

y=− 1/2 x+1017