Question

a water tank holds 18000 gallons. How long will it take for the water level to reach 6000 gallons if the water is used at an average rate of 450 gallons per day.I need slope, y intercept and equation

Answer 1

Given the information, we know that the tank starts holding 18000 gallons of water. Then after 1 day passes, the tank now holds 18000-450=17550 gallons of water. With this, we can find the slope and the equation required:

`\begin{gathered} (0,18000),(1,17550) \\ m=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow m=(17550-18000)/(1-0)=-(450)/(1)=-450 \end{gathered}`

Now, using y=mx+b, we have the following equation:

`y=-450x+18000`

Finally, to know how long will it take to reach 6000 gallons, we make y=6000 and solve for x:

`\begin{gathered} y=6000 \\ \Rightarrow6000=-450x+18000 \\ \Rightarrow450x=18000-6000=12000 \\ \Rightarrow x=(12000)/(450)=26.67 \\ x=26.67 \end{gathered}`

Therefore, it will take 26.67 days to reach 6000 gallons of water