The equation you've provided, \( y = -7.5x + 45 \), describes the height \( y \) of the water balloon in feet (or another unit of height) as a function of time \( x \) in seconds. Here’s what we can derive from this equation:
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Initial Height: When the balloon is thrown (at \( x = 0 \)), the height \( y \) is: \[ y = -7.5(0) + 45 = 45 \text{ feet} \] This means the balloon is thrown from a height of 45 feet.
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Slope Interpretation: The coefficient of \( x \) is \(-7.5\), which indicates the rate of change of height with respect to time. In this case, it means that for each second the balloon is in the air, it falls 7.5 feet.
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Finding when the balloon hits the ground: To find when the balloon hits the ground, set \( y = 0 \): \[ 0 = -7.5x + 45 \] Solving for \( x \): \[ 7.5x = 45 \ x = \frac{45}{7.5} = 6 \text{ seconds} \] This means the balloon will hit the ground after 6 seconds.
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Graphing the equation: If you were to graph this equation, you'd plot the height \( y \) on the vertical axis and time \( x \) on the horizontal axis. The graph would be a straight line that starts at (0, 45) and has a downward slope, crossing the x-axis at (6, 0).
If you have any specific questions about this scenario or would like to explore further aspects, feel free to ask!
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