Question

the taieri plain in new zealand is 6 feet below sea level (or $-6$ feet). if you are standing 3 feet above sea level, is your elevation the opposite of the elevation of the plain? describe the steps you would follow with a vertical number line to find the answer.

Explanation:

Step1: Define opposite elevation

The opposite of an elevation $x$ is $-x$. For the plain's elevation of $-6$ feet, its opposite is $-(-6) = 6$ feet.

Step2: Mark values on number line

1. Draw a vertical number line, label 0 as sea level, positive numbers above 0 (above sea level), negative numbers below 0 (below sea level).
2. Plot the plain's elevation: $-6$ (6 units below 0).
3. Plot your elevation: $3$ (3 units above 0).
4. Plot the opposite of the plain's elevation: $6$ (6 units above 0).

Step3: Compare elevations

Compare your elevation ($3$) to the opposite of the plain's elevation ($6$). Since $3
eq 6$, they are not opposites.

Answer:

No, your elevation is not the opposite of the plain's elevation.
To verify with a vertical number line:

1. Label 0 as sea level, positive values upward (above sea level) and negative values downward (below sea level).
2. Plot the Taieri Plain at $-6$ (6 units below 0).
3. The opposite of $-6$ is $6$, so plot this 6 units above 0.
4. Plot your elevation at $3$ (3 units above 0).
5. Since $3$ does not match $6$, your elevation is not the opposite of the plain's elevation.