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 for the relationship between time (x) in minutes and distance (y) in feet, we need to analyze the data in the table.

From the table:
- 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 a constant amount as time (x) increases. Let's determine the rate of change:

Calculating the change in distance for each minute:
- 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 each additional minute.

This suggests a linear relationship, which can be expressed in the form:
\[ y = mx + b \]
where \( m \) is the slope (rate of change) and \( b \) is the y-intercept.

Here, we have established that:
- \( m = 75 \) (the increase in distance per minute)
- To find \( b \), we can use one of the points. When \( x = 0 \) (which is not in our table, but we can deduce), the distance \( y \) would be 0.

Thus, the formula becomes:
\[ y = 75x \]

Therefore, the formula that relates time (x) in minutes to distance (y) in feet is:
\[
y = 75x
\]