To create a formula that relates time (X) in minutes to distance (Y) in feet, we can observe the data provided in the table.
You have the following pairs of (X, Y):
- When \( X = 1 \), \( Y = 75 \)
- When \( X = 2 \), \( Y = 150 \)
- When \( X = 3 \), \( Y = 225 \)
- When \( X = 4 \), \( Y = 300 \)
From this data, we can notice that the distance increases linearly as time increases.
To derive a formula, we can find the relationship between X and Y:
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Determine the slope (m): The slope can be found by taking any two points. Let’s take the points \( (1, 75) \) and \( (2, 150) \): \[ m = \frac{Y_2 - Y_1}{X_2 - X_1} = \frac{150 - 75}{2 - 1} = \frac{75}{1} = 75 \]
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Use the point-slope form of the line: The point-slope form of a linear equation is given by: \[ Y - Y_1 = m(X - X_1) \] Using the point \( (1, 75) \): \[ Y - 75 = 75(X - 1) \]
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Simplifying this gives: \[ Y - 75 = 75X - 75 \ Y = 75X \]
So, the formula that relates time (X in minutes) to distance (Y in feet) is: \[ Y = 75X \]
This means that for every minute that passes, the distance increases by 75 feet.
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