Question

X will represent time in minutes, while y will represent the distance in feet

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

Use the table to create a formula for the given information

Answer 1

To create a formula that relates time (X) in minutes to distance (Y) in feet, we can observe the data provided in the table.

You have the following pairs of (X, Y):

- When \( X = 1 \), \( Y = 75 \)
- When \( X = 2 \), \( Y = 150 \)
- When \( X = 3 \), \( Y = 225 \)
- When \( X = 4 \), \( Y = 300 \)

From this data, we can notice that the distance increases linearly as time increases.

To derive a formula, we can find the relationship between X and Y:

1. **Determine the slope (m):**
The slope can be found by taking any two points. Let’s take the points \( (1, 75) \) and \( (2, 150) \):
\[
m = \frac{Y_2 - Y_1}{X_2 - X_1} = \frac{150 - 75}{2 - 1} = \frac{75}{1} = 75
\]

2. **Use the point-slope form of the line:**
The point-slope form of a linear equation is given by:
\[
Y - Y_1 = m(X - X_1)
\]
Using the point \( (1, 75) \):
\[
Y - 75 = 75(X - 1)
\]

3. **Simplifying this gives:**
\[
Y - 75 = 75X - 75 \\
Y = 75X
\]

So, the formula that relates time (X in minutes) to distance (Y in feet) is:
\[
Y = 75X
\]

This means that for every minute that passes, the distance increases by 75 feet.