Question

Mr. Mole left his burrow and started digging his way down at a constant rate. Time (minutes) Altitude (meters) 666 -20.4−20.4minus, 20, point, 4 999 -27.6−27.6minus, 27, point, 6 121212 -34.8−34.8minus, 34, point, 8 What is the altitude of Mr. Mole's burrow?

Answer 1

its 6 not -6

Explanation:

Answer 2

`-6` meters.

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:

`m=(y_2-y_1)/(x_2-x_1)`, where,

`y_2-y_1` represents difference of two y-coordinates,

`x_2-x_1` represents difference of two corresponding x-coordinates of y-coordinates.

Let
`(6,-20.4)` be
`(x_1,y_1)` and
`(9,-27.6)` be
`(x_2,y_2)`.

`m=(-27.6-(-20.4))/(9-6)`

`m=(-27.6+20.4)/(3)`

`m=(-7.2)/(3)`

`m=-2.4`

Now, we will use slope-intercept form of equation to find altitude of Mr. Mole's burrow.

`y=mx+b`, where,

m = Slope,

b = The initial value or the y-intercept.

Upon substituting
`m=-2.4` and coordinates of point
`(6,-20.4)`, we will get:

`-20.4=-2.4(6)+b`

`-20.4=-14.4+b`

`-20.4+14.4=-14.4+14.4+b`

`-6=b`

Since in our given case y-intercept represents the altitude of Mr. Mole's burrow, therefore, the altitude of Mr. Mole's burrow is
`-6` meters.