Question

Mr. Mole left his burrow that lies below the ground and started digging his way at a constant rate deeper into the ground. Let y represent Mr. Mole's altitude (in meters) relative to the ground after x minutes. Which of the following could be the graph of the relationship?

Answer 1

We know that:

The initial conditions are -7 meters at 0 minutes.

Then, after 6 minutes, he was 16 meters below the ground.

According to these two simple facts we can found the linear function that describes this problem. First, the problem says that Mr. Mole is descending at a constant rate, which is the slope of the function. Now, to calculate the slope we need to points, which are and , where t-values are minutes, and y-values are meters. You can see, that the first point is the initial condition and the second point is 6 minutes later.

So, we calculate the slope:

From the slope we can see that Mr. Mole is descending, because it has a negative sign. Also, the point is on the y-axis, because t is null, so -7 is part of the function. Therefore the function that describes this problem is:

Explanation: