Answer:
meters.
Step-by-step explanation:
We have been given Mr. Mole left his burrow and started digging his way down at a constant rate.
We are also given a table of data as:
Time (minutes) Altitude (meters)
6 -20.4
9 -27.6
12 -34.8
First of all, we will find Mr. Mole's digging rate using slope formula and given information as:
, where,
represents difference of two y-coordinates,
represents difference of two corresponding x-coordinates of y-coordinates.
Let
be
and
be
.
![m=\frac{-27.6-(-20.4)}{9-6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-27.6-%28-20.4%29%7D%7B9-6%7D)
![m=\frac{-27.6+20.4}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-27.6%2B20.4%7D%7B3%7D)
![m=\frac{-7.2}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-7.2%7D%7B3%7D)
![m=-2.4](https://tex.z-dn.net/?f=m%3D-2.4)
Now, we will use slope-intercept form of equation to find altitude of Mr. Mole's burrow.
, where,
m = Slope,
b = The initial value or the y-intercept.
Upon substituting
and coordinates of point
, we will get:
![-20.4=-2.4(6)+b](https://tex.z-dn.net/?f=-20.4%3D-2.4%286%29%2Bb)
![-20.4=-14.4+b](https://tex.z-dn.net/?f=-20.4%3D-14.4%2Bb)
![-20.4+14.4=-14.4+14.4+b](https://tex.z-dn.net/?f=-20.4%2B14.4%3D-14.4%2B14.4%2Bb)
![-6=b](https://tex.z-dn.net/?f=-6%3Db)
Since in our given case y-intercept represents the altitude of Mr. Mole's burrow, therefore, the altitude of Mr. Mole's burrow is
meters.