Question

Time (minutes) 1 2 3 4
Distance (feet) 75 150 225 300

Use the table to create a formula for the given information. X will represent time in minutes, while y will represent the distance in feet

Answer 1

To find a formula that relates distance \( y \) in feet to time \( x \) in minutes, we can observe the pattern from the table you've provided. Here are the values:

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

From the data, we can see that for each additional minute, the distance increases by 75 feet. This indicates a linear relationship.

To formulate this as a linear equation \( y = mx + b \):
- \( m \), the slope, is the change in distance per minute, which is 75 feet.
- \( b \), the y-intercept (the distance when \( x = 0 \)), can be determined by using one of the points.

We can use the point (1, 75):

\[
y = mx + b
\]
\[
75 = 75(1) + b
\]
\[
75 = 75 + b
\]
\[
b = 0
\]

Thus, the equation simplifies to:

\[
y = 75x
\]

So, the formula relating distance \( y \) in feet to time \( x \) in minutes is:

\[
y = 75x
\]