To create a formula that represents the relationship between time (x) in minutes and distance (y) in feet based on the provided data, we first need to observe the values given in the table.
From the table:
| Time (Minutes), x | Distance (Feet), y | |-------------------|--------------------| | 1 | 75 | | 2 | 150 | | 3 | 225 | | 4 | 300 |
We can see that for each minute increase in time, the distance increases by 75 feet. This indicates a linear relationship between x and y.
To find the formula, we can use the slope-intercept form of a linear equation: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept.
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Calculate the slope (m): The slope \( m \) can be calculated as the change in distance divided by the change in time. From the data, we can see that every minute (1 unit of x), the distance (y) increases by 75 feet.
So, \( m = 75 \).
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Determine the y-intercept (b): By examining the table, when \( x = 0 \), the distance \( y \) would be \( 0 \) feet (since it makes sense that if no time has passed, no distance has been covered). Thus \( b = 0 \).
Putting it all together, the formula relating distance \( y \) to time \( x \) is:
\[ y = 75x \]
This formula indicates that for every minute of time, the distance is 75 feet.
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