Solution:
Given:
To get the equation, we pick two points to get the rate of change of depth per day.
Using the points (1,18) and (2,17.5), then
[tex]\begin{gathered} slope,m=\frac{y_2-y_1}{x_2-x_1} \\ where; \\ x_1=1,y_1=18 \\ x_2=2,y_2=17.5 \\ \\ Hence, \\ m=\frac{17.5-18}{2-1} \\ m=-\frac{0.5}{1} \\ m=-0.5 \\ m=-\frac{1}{2} \end{gathered}[/tex]
Using the form of a linear equation,
[tex]\begin{gathered} y=mx+b \\ Using\text{ the point }(1,18), \\ x=1 \\ y=18 \\ m=-0.5 \\ \\ 18=-0.5(1)+b \\ 18=-0.5+b \\ 18+0.5=b \\ b=18.5 \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} m=-\frac{1}{2} \\ b=18.5 \\ \\ Using\text{ the equation;} \\ y=mx+b \end{gathered}[/tex]
Therefore, the equation that shows the water depth, y in the fish tank after x days is;
[tex]y=-\frac{1}{2}x+18.5[/tex]
