To create a formula that relates time \( x \) (in minutes) to distance \( y \) (in feet), we can analyze the provided data points:
- When \( x = 1 \), \( y = 75 \)
- When \( x = 2 \), \( y = 150 \)
- When \( x = 3 \), \( y = 225 \)
- When \( x = 4 \), \( y = 300 \)
From the data, we see a clear relationship where each time increment adds a consistent distance. Specifically, \( y \) increases by \( 75 \) feet for each \( 1 \) minute increment of \( x \).
We can express this relationship as a linear equation in the form of \( y = mx + b \), where:
- \( m \) is the slope (the change in \( y \) per unit change in \( x \))
- \( b \) is the y-intercept (the value of \( y \) when \( x = 0 \))
From the relationship observed:
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Calculate the slope \( m \): \[ m = \frac{\Delta y}{\Delta x} = \frac{75}{1} = 75 \]
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Determine the y-intercept \( b \): Since when \( x = 0 \), \( y \) would be \( 0 \) (as we assume starting from zero distance when time = 0), we can set \( b = 0 \).
Thus, our linear equation is:
\[ y = 75x \]
This formula states that for every minute \( x \), the distance \( y \) is \( 75 \) feet.