Question

Use the table to answer the question.

Let x represent the time in minutes and let y represent the distance in feet.

Time (Minutes), x 1 2 3 4
Distance (Feet), y 75 150 225 300
Use the table to create a formula for the given information.

(1 point)

Answer 1

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.