As an elementary teacher, you may teach science as well. Upper elementary students will probably learn about how pressure is related to distance above sea level. Although air pressure fluctuates because of weather conditions, standard normal or average air pressure at sea level is 14.7 pounds per square inch. Standard air pressure in Denver at approximately 5280 feet (a mile high) is 12.1 pounds per square inch. A linear function describes this relationship.

a. Use the given two points to write an algebraic equation that relates the distance above sea level with the air pressure. Is this relationship proportional?

b. At 66 feet below sea level, the pressure equals 44.1 pounds per square inch. At 99 feet below sea level, the pressure equals 58.8 pounds per square inch. How are the quantities of depth and pressure related? Is this relationship proportional? (Hint: The change is constant.)

The pressure under the sea level also forms a non-proportional relationship with the equation y = 0.70909x - 3.7, where x is the depth below seal level and y is the pressure.

In order to find an equation for the air pressure based on altitude, we need two points which we have: (0, 14.7) for sea level and (5280, 12.1) for Denver. A Linear Function can be written in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

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

m = (y₂ - y₁) / (x₂ - x₁)

which results in m=(12.1-14.7)/(5280-0), or m= -0.0004924 and to calculate the y-intercept (b), simply substitute m, x₁ and y₁ into the equation, or b=14.7.

Thus, the equation relating altitude and pressure is y = -0.0004924x +14.7.

This equation suggests a non-proportional relationship as the y-intercept is not zero.

For pressure under the sea, using the points (66, 44.1) and (99, 58.8), again calculate the slope (m) = (58.8-44.1)/(99-66) gives m=0.70909.

Substituting for b, we get b = 44.1 - 0.70909 * 66 which gives b= -3.7 approximately.

Therefore, the equation for underwater pressure is y = 0.70909x - 3.7.

As with altitude, this relationship is also non-proportional as the y-intercept is not zero.

Learn more about the topic of Linear Function here:

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