Let's find the equation of the line relating "t" and "S".
The formula we are going to use is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Where
(x1, y1) and (x2, y2) are two points through which the line goes through
Note: We are going to use "t" and "S" in place of "x" and "y" later
Let's take 2 points from the table of values:
[tex]\begin{gathered} (x_1,y_1)=(2,9) \\ \text{and} \\ (x_2,y_2)=(5,4.5) \\ \end{gathered}[/tex]
Now, let's substitute these values and find the equation of the line. The steps are outlined below:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-9=\frac{4.5-9}{5-2}(x-2) \\ y-9=\frac{-4.5}{3}(x-2) \\ y-9=-1.5(x-2) \\ y-9=-1.5x+3 \\ y=-1.5x+3+9 \\ y=-1.5x+12 \end{gathered}[/tex]
In terms of "t" and "S", we can write >>>
[tex]S=-1.5t+12[/tex]
We want the time (t) it will take for depth (S) of snow to be 3.75 inches.
So, we put "3.75" into S and solve for "t". Shown below:
[tex]\begin{gathered} S=-1.5t+12 \\ 3.75=-1.5t+12 \\ 1.5t=12-3.75 \\ 1.5t=8.25 \\ t=\frac{8.25}{1.5} \\ t=5.5 \end{gathered}[/tex]Answer5.5 hours
