Question

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)
Remaining Attempts : 3
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Answer 1

To create a formula relating time \( x \) (in minutes) to distance \( y \) (in feet), we can start by observing the data provided in the table:

\[
\begin{array}{|c|c|}
\hline
\text{Time (Minutes), } x & \text{Distance (Feet), } y \\
\hline
1 & 75 \\
2 & 150 \\
3 & 225 \\
4 & 300 \\
\hline
\end{array}
\]

From the data, you can see that as the time increases by 1 minute, the distance increases by 75 feet. This indicates a linear relationship between \( x \) and \( y \).

To derive the linear equation, we can use the slope-intercept form of a line, which is expressed as:

\[
y = mx + b
\]

Where \( m \) represents the slope and \( b \) is the y-intercept.

1. **Finding the slope \( m \)**:
\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{150 - 75}{2 - 1} = \frac{75}{1} = 75
\]

2. **Finding the y-intercept \( b \)**:
When \( x = 0 \), \( y \) can be calculated by observing the relation:
\[
y = mx + b \implies y = 75(0) + b \implies y = b
\]
However, since there is no data at \( x = 0 \), we can simply use one of the points. Let's use \( (1, 75) \) to find \( b \):
\[
75 = 75(1) + b \implies 75 = 75 + b \implies b = 0
\]

3. **Final Equation**:
Putting it all together, the formula that relates \( x \) and \( y \) is:
\[
y = 75x
\]

Thus, the formula that represents the relationship between time in minutes \( x \) and distance in feet \( y \) is:

\[
y = 75x
\]