Question

A faucet is used to add water to a large bottle that already contained some water.After it has been filled for 3 seconds, the gauge on the bottle indicates that itcontains 9 ounces of water. After it has been filled for 11 seconds, the gaugeindicates the bottle contains 25 ounces of water. Let y be the amount of water inthe bottle x seconds after the faucet was turned on. Write an equation thatmodels the amount of water in the bottle in terms of x.

Answer 1

Given the word problem, we can deduce the following information:

1. After it has been filled for 3 seconds, the gauge on the bottle indicates that it

contains 9 ounces of water.

2. After it has been filled for 11 seconds, the gauge indicates the bottle contains 25 ounces of water.

Based on the given information, it gives us points for (x,y) and they are (3,9) and (11,25). To determine the equation that models the amount of water in the bottle in terms of x, we use the slope formula:

We let:

We plug in what we know:

`\begin{gathered} m=(25-9)/(11-3) \\ \text{Simplify} \\ m=2 \end{gathered}`

Next, we use the point slope formula to get the equation:

Then, we plug in m=2, x=3 and y=9 into the formula:

`\begin{gathered} y-9=2(x-3) \\ \text{Simplify and rearrange} \\ y-9=2x-6 \\ y=2x-6+9 \\ y=2x+3 \end{gathered}`

Therefore, the equation that models the amount of water in the bottle in terms of x is y=2x+3.