Given:
Initial ice sheet's thickness = 2 meter
After 3 weeks, the ice sheet's thickness = 1.25 meters
To find:
The equation for the relationship between the thickness and number of weeks.
Solution:
Let y represent the ice sheet's thickness (in meters) after x weeks.
Initial ice sheet's thickness = 2 meter
It means, the equation of relation must be satisfy by the point (0,2).
After 3 weeks, the ice sheet's thickness = 1.25 meters
It means, the equation of relation must be satisfy by the point (3,1.25).
If a linear function passes through two points, then the equation is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-2=\dfrac{1.25-2}{3-0}(x-0)[/tex]
[tex]y-2=\dfrac{-0.75}{3}x[/tex]
[tex]y-2=-0.25x[/tex]
Add 2 on both sides.
[tex]y=-0.25x+2[/tex]
Therefore, the required equation for the given relation is [tex]y=-0.25x+2[/tex].
