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.

Answer 1

To derive a formula from the given data, we can observe the relationship between time (x) and distance (y).

From the table, we can summarize the data as follows:

- 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 time \( x \) increases, the distance \( y \) also increases. The pattern demonstrates a linear relationship.

To find the formula, let’s first determine the rate of change (slope) between the points:

The distance increased by 75 feet for each additional minute (from 75 to 150 feet, etc.).

Now, this gives us a slope \( m = 75 \) feet/minute.

The general formula for a linear relationship is:

\[
y = mx + b
\]

Where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

To find \( b \), we can substitute one of the points into the equation. Let's use the point \( (1, 75) \):

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

Thus, the formula is:

\[
y = 75x
\]

This means that for every minute of time \( x \), the distance \( y \) will be \( 75 \times x \) feet.