To create a formula based on the provided table, we first observe the relationship between \( x \) (time in minutes) and \( y \) (distance in feet).
Given the data:
- 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 75 feet for each additional minute. This indicates a linear relationship, where the rate of change (slope) is constant.
To find the slope \( m \):
\[ m = \frac{\Delta y}{\Delta x} = \frac{150 - 75}{2 - 1} = \frac{75}{1} = 75 \]
This shows that for every 1 minute (for each increment of \( x \)), the distance \( y \) increases by 75 feet.
Next, we can use the slope-intercept form of a linear equation, which is given by:
\[ y = mx + b \]
Where:
- \( m = 75 \) (the slope)
- \( b \) is the y-intercept (the value of \( y \) when \( x = 0 \)).
To find \( b \), we can look at one of the given points. When \( x = 1 \) and \( y = 75 \):
\[ 75 = 75(1) + b \] \[ 75 = 75 + b \] \[ b = 75 - 75 = 0 \]
Now we can plug in the values of \( m \) and \( b \) into the equation:
\[ y = 75x + 0 \]
Thus, the formula relating distance to time in this case is:
\[ y = 75x \]