The graph shows the relationship between the amount of water that flows from a fountain and time. Enter a number in the box to complete the equation that represents the amount of w... The graph shows the relationship between the amount of water that flows from a fountain and time. Enter a number in the box to complete the equation that represents the amount of water that flows after x minutes.
Understand the Problem
The question involves interpreting a graph that shows the relationship between the amount of water flowing from a fountain and time. The task is to determine the missing number in the equation that represents this relationship, given the information from the graph.
Answer
The equation is $y = 250x$.
Answer for screen readers
The missing number in the equation is 250. Thus, the equation is $y = 250x$.
Steps to Solve
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Identify the Variables The variable $y$ represents the amount of water in gallons, and $x$ represents the time in minutes.
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Determine the Slope From the graph, identify two points on the line. For example, at $x = 0$, $y = 0$ (the origin), and at $x = 6$, $y = 1500$ gallons.
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Calculate the Rate of Flow The slope (rate of change) can be calculated using the formula: $$ \text{slope} = \frac{\Delta y}{\Delta x} $$ For the points (0, 0) and (6, 1500): $$ \text{slope} = \frac{1500 - 0}{6 - 0} = \frac{1500}{6} = 250 $$
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Formulate the Equation Now that we have the slope, substitute it into the equation $y = mx$: $$ y = 250x $$
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Fill in the Missing Number The equation to complete is $y = \underline{250} x$.
The missing number in the equation is 250. Thus, the equation is $y = 250x$.
More Information
This equation indicates that 250 gallons of water flow from the fountain for each minute that passes. This means that after six minutes, a total of 1500 gallons would have flowed.
Tips
One common mistake is misreading the graph, especially in identifying the scale of the axes, which can lead to incorrect slope calculations. To avoid this, always double-check the numbers on the axes.
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