To create a formula that relates the time \( x \) in minutes to the distance \( y \) in feet based on the data provided, we can observe the relationship between \( x \) and \( y \) from the table:
- When \( x = 1 \), \( y = 75 \)
- When \( x = 2 \), \( y = 150 \)
- When \( x = 3 \), \( y = 225 \)
- When \( x = 4 \), \( y = 300 \)
From this, we can see that as \( x \) increases by 1, \( y \) increases by 75 feet. This indicates a direct linear relationship.
We can express this linear relationship in the formula \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
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Find the slope \( m \): \[ m = \frac{\Delta y}{\Delta x} = \frac{150 - 75}{2 - 1} = \frac{75}{1} = 75 \]
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Find the y-intercept \( b \): Since the distance at \( x = 0 \) (which is not listed in the table) would logically be 0, we have \( b = 0 \).
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Write the formula: The relationship between distance \( y \) and time \( x \) can be expressed as: \[ y = 75x \]
Thus, the formula that relates the time \( x \) in minutes to the distance \( y \) in feet is: \[ y = 75x \]
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