To represent the proportional relationship between the amount of water (in cups) and the time (in seconds) it takes to fill that water, we can define the relationship as follows:
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Determine the Constant of Proportionality: Given that it takes 3 seconds to fill 1 cup of water, we can state the relationship mathematically as: \[ y = 3x \] where \(y\) is the time in seconds and \(x\) is the amount of water in cups.
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Select Points: To graph this relationship, we can select two values for \(x\) to find corresponding \(y\) values.
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For \(x = 1\) (1 cup of water): \[ y = 3(1) = 3 \quad \Rightarrow \quad (1, 3) \]
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For \(x = 2\) (2 cups of water): \[ y = 3(2) = 6 \quad \Rightarrow \quad (2, 6) \]
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Points to Plot: So the two points we can plot on a graph are:
- Point 1: \((1, 3)\)
- Point 2: \((2, 6)\)
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Graph the Points: To graph the relationship:
- On the x-axis, mark the amounts of water in cups (1, 2, etc.).
- On the y-axis, mark the time in seconds (3, 6, etc.).
- Plot the two points, \((1, 3)\) and \((2, 6)\).
- Draw a straight line through these two points, extending in both directions to emphasize the linear relationship.
- Graph Description: This will result in a straight line starting from the origin (0,0) and passing through the points (1,3) and (2,6), demonstrating that as the amount of water increases, the time taken increases proportionately.
In conclusion, the resulting graph visually illustrates the proportional relationship between the amount of water Wendy fills in her bottle and the time it takes.
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