Respuesta :
Answer:
[tex]-6[/tex] 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:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where,
[tex]y_2-y_1[/tex] represents difference of two y-coordinates,
[tex]x_2-x_1[/tex] represents difference of two corresponding x-coordinates of y-coordinates.
Let [tex](6,-20.4)[/tex] be [tex](x_1,y_1)[/tex] and [tex](9,-27.6)[/tex] be [tex](x_2,y_2)[/tex].
[tex]m=\frac{-27.6-(-20.4)}{9-6}[/tex]
[tex]m=\frac{-27.6+20.4}{3}[/tex]
[tex]m=\frac{-7.2}{3}[/tex]
[tex]m=-2.4[/tex]
Now, we will use slope-intercept form of equation to find altitude of Mr. Mole's burrow.
[tex]y=mx+b[/tex], where,
m = Slope,
b = The initial value or the y-intercept.
Upon substituting [tex]m=-2.4[/tex] and coordinates of point [tex](6,-20.4)[/tex], we will get:
[tex]-20.4=-2.4(6)+b[/tex]
[tex]-20.4=-14.4+b[/tex]
[tex]-20.4+14.4=-14.4+14.4+b[/tex]
[tex]-6=b[/tex]
Since in our given case y-intercept represents the altitude of Mr. Mole's burrow, therefore, the altitude of Mr. Mole's burrow is [tex]-6[/tex] meters.
