To find a formula that relates distance \( y \) in feet to time \( x \) in minutes, we can observe the pattern from the table you've provided. Here are the values:
- When \( x = 1 \), \( y = 75 \)
- When \( x = 2 \), \( y = 150 \)
- When \( x = 3 \), \( y = 225 \)
- When \( x = 4 \), \( y = 300 \)
From the data, we can see that for each additional minute, the distance increases by 75 feet. This indicates a linear relationship.
To formulate this as a linear equation \( y = mx + b \):
- \( m \), the slope, is the change in distance per minute, which is 75 feet.
- \( b \), the y-intercept (the distance when \( x = 0 \)), can be determined by using one of the points.
We can use the point (1, 75):
\[ y = mx + b \] \[ 75 = 75(1) + b \] \[ 75 = 75 + b \] \[ b = 0 \]
Thus, the equation simplifies to:
\[ y = 75x \]
So, the formula relating distance \( y \) in feet to time \( x \) in minutes is:
\[ y = 75x \]
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