Question

Simon measures the depth of water in centimeters, in his fish tank at the end of each day. His measurements are shown. Which equation shows the water depth, y, in the fish tank after x days?

Answer 1

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

`\begin{gathered} slope,m=(y_2-y_1)/(x_2-x_1) \\ where; \\ x_1=1,y_1=18 \\ x_2=2,y_2=17.5 \\ \\ Hence, \\ m=(17.5-18)/(2-1) \\ m=-(0.5)/(1) \\ m=-0.5 \\ m=-(1)/(2) \end{gathered}`

Using the form of a linear equation,

`\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}`

Hence,

`\begin{gathered} m=-(1)/(2) \\ b=18.5 \\ \\ Using\text{ the equation;} \\ y=mx+b \end{gathered}`

Therefore, the equation that shows the water depth, y in the fish tank after x days is;

`y=-(1)/(2)x+18.5`