It is given that the pond already has 600 liters of water and that it is filled at a rate of 30 liters per minute.
It is required to find and graph the equation relating W, the amount of water in the pond, and T, the number of minutes.
Since water is added into the pond at a constant rate, it follows that the equation must be the equation of a line:
[tex]W=mT+c[/tex]
Where m is the rate at which water is added in liters per minute, and c is the amount of water in liters already in the pond.
Hence, substitute m=30 and c=600 into the equation:
[tex]W=30T+600[/tex]
To graph the equation, find two points (T, W) that satisfy the equation.
Substitute T=0 into the equation:
[tex]\begin{gathered} W=30(0)+600 \\ \Rightarrow W=0+600 \\ \Rightarrow W=600 \end{gathered}[/tex]
Hence, one point is (0,600).
Substitute T=1 to find another point:
[tex]W=30(1)+600=30+600=630[/tex]
Another point is (1,600).
Graph these points and join them with a straight line:
The required equation is W=30T+600.
The graph is shown above.
