To create a formula that represents the relationship between time (x) in minutes and distance (y) in feet based on the table provided, we first observe the values given:
- When \( x = 1 \), \( y = 75 \)
- When \( x = 2 \), \( y = 150 \)
- When \( x = 3 \), \( y = 225 \)
- When \( x = 4 \), \( y = 300 \)
We can see that as \( x \) increases by 1, \( y \) increases by 75. This suggests a linear relationship between \( x \) and \( y \).
The relationship can be expressed in the form of a linear equation: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept.
From our observations:
- Slope \( m = 75 \) (since 75 feet is added for each additional minute).
- To find the y-intercept \( b \), we can use one of the points. Let’s use the point (1, 75):
Setting up the equation using point (1, 75): \[ 75 = 75(1) + b \]
Solving for \( b \): \[ 75 = 75 + b \ b = 0 \]
Thus, the final formula for the distance \( y \) as a function of time \( x \) is: \[ y = 75x \]
This formula indicates that for every minute, the distance increases by 75 feet.
1 answer