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

Answer 1

To create a formula for the relationship between time (x) and distance (y) based on the given data, we can observe the pattern in the table.

The data points are as follows:

- When \( x = 1 \), \( y = 75 \)
- When \( x = 2 \), \( y = 150 \)
- When \( x = 3 \), \( y = 225 \)
- When \( x = 4 \), \( y = 300 \)

To find the formula, we can first identify the slope of the relationship:

1. Calculate the change in y for each change in x:
- 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 every 1 minute increase in time.

Thus, the relationship can be described as a linear equation of the form:

\[
y = mx + b
\]

Where:
- \( m \) is the slope (which is 75 in this case),
- \( b \) is the y-intercept (the value of y when x = 0).

Since all the points reveal consistent increases, we can calculate the y-intercept \( b \).

Using the first point (1, 75):
- Plug in the values to find \( b \):

\[
75 = 75(1) + b
\]
\[
75 = 75 + b \rightarrow b = 0
\]

Therefore, the equation that describes the relationship between time and distance is:

\[
y = 75x
\]

This formula indicates that for every minute (x), the distance (y) increases by 75 feet.