The relationship between the amount of water \(x\) (in cups) that Wendy puts in her bottle and the time \(y\) (in seconds) it takes can be expressed with the equation derived from the given information.
Since it takes 3 seconds to fill 1 cup of water, we can establish the proportional relationship as follows:
\[ y = k \cdot x \]
where \(k\) is the constant of proportionality. From the information provided, we know that:
\[ k = 3 \text{ seconds per cup} \]
Thus the equation becomes:
\[ y = 3x \]
In this equation:
- \(y\) is the time in seconds,
- \(x\) is the amount of water in cups.
This means that if Wendy wants to fill her bottle with a certain number of cups of water, you can multiply that number by 3 to find out how many seconds it will take. For example:
- If \(x = 1\) cup, then \(y = 3 \times 1 = 3\) seconds.
- If \(x = 2\) cups, then \(y = 3 \times 2 = 6\) seconds.
- If \(x = 3\) cups, then \(y = 3 \times 3 = 9\) seconds.
And so forth, demonstrating the linear and proportional relationship between the amount of water and the time taken to fill it.
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