To create a formula for the relationship between time (x) in minutes and distance (y) in feet, we need to analyze the data in the table.
From 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 the distance (y) increases by a constant amount as time (x) increases. Let's determine the rate of change:
Calculating the change in distance for each minute:
- From \( x = 1 \) to \( x = 2 \): \( 150 - 75 = 75 \)
- From \( x = 2 \) to \( x = 3 \): \( 225 - 150 = 75 \)
- From \( x = 3 \) to \( x = 4 \): \( 300 - 225 = 75 \)
The distance increases by 75 feet for each additional minute.
This suggests a linear relationship, which can be expressed in the form: \[ y = mx + b \] where \( m \) is the slope (rate of change) and \( b \) is the y-intercept.
Here, we have established that:
- \( m = 75 \) (the increase in distance per minute)
- To find \( b \), we can use one of the points. When \( x = 0 \) (which is not in our table, but we can deduce), the distance \( y \) would be 0.
Thus, the formula becomes: \[ y = 75x \]
Therefore, the formula that relates time (x) in minutes to distance (y) in feet is: \[ y = 75x \]
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