Question

Mr. Mole's burrow lies 5 meters below the ground. He started digging his way deeper into the ground, descending 3 meters each minute. Graph the relationship between Mr. Mole's elevation relative to the ground (in meters) and time (in minutes). Elevation (meters) 2 4. 8 10 12 14 16 18 Time (minutes) 5+ -10 --15 -20 -25 -30 -35- -40+ -45+

Answer 1

Let y represent the elevation in meters, then "zero" represents the ground levels, then the depth is represented by the negative numbers. The deeper he digs, the more negative the elevation will be.

X represents the time in minutes.

If the burrow is 5 meters below ground, in the coordinate system its location is at point (0,-5) → at time zero he didn't start digging yet.

Then he starts digging at a rate of 3meters/minute. The decrease in elevation is expressed by making the digging rate negative -3m/min → this rate is the slope of the line, it indicates the depth variation for each passing minute.

The line that shows the relationship between the depth and the time is:

`y=-3x-5`

To plot the line you have to determine two lines of it and then link them.

One can be the starting point, i.e. the y-intercept (0,-5)

For the second one just choose any value of time and replace it on the equation.

For example for x=4min

`\begin{gathered} y=-3\cdot4-5 \\ y=-17 \end{gathered}`

The second point is (4,-17)