To create a formula that represents the relationship between time (x) and distance (y), we can observe the values provided in the table:
- When \( x = 1 \), \( y = 75 \)
- When \( x = 2 \), \( y = 150 \)
- When \( x = 3 \), \( y = 225 \)
- When \( x = 4 \), \( y = 300 \)
We can see that for every increase of 1 minute in time, the distance increases by 75 feet. This indicates a linear relationship.
To derive the formula, we can express this relationship as:
\[ y = mx + b \]
Where \( m \) is the slope (the rate of change of distance with respect to time) and \( b \) is the y-intercept.
From the values given:
- The slope \( m = 75 \) feet per minute (since \( y \) increases by 75 feet for every 1 minute increase in \( x \)).
- The y-intercept \( b \) is 0 (when \( x = 0 \), \( y = 0 \)).
Thus, the formula relating distance to time can be expressed as:
\[ y = 75x \]
This formula indicates that the distance \( y \) in feet is 75 times the time \( x \) in minutes.
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