Question

Mr. Mole left his burrow that lies 7 meters below the ground and started digging his way deeper into the ground, descending at a constant rate. After 6 minutes, he was 16 meters below the ground.

Let A represent Mr. Mole's altitude (in meters) relative to the ground after t minutes.

Complete the equation for the relationship between the altitude and number of minutes.


A=

Answer 1

`A=-1.5t-7`

Explanation:

Let

A ----->Mr. Mole's altitude (in meters)

t ----> the time in minutes

we know that

Mr. Mole is descending at a constant rate, so we have a linear relationship

we have the points

For t=0 min, A=-7 m -----> point (0,-7) ----> A-intercept (value of A when the value of t is equal to zero)

For t=6 min, A=-16 m -----> point (6,-16)

Find the slope of the linear equation

`m=(-16+7)/(6-0)=-9/6=-1.5`

Find the linear equation in slope intercept form

`A=mt+b`

we have

`m=-1.5\\b=-7`

substitute

`A=-1.5t-7`