To determine if John’s claim is correct, we need to find the slopes of both Line 1 and Line 2. If the slopes of the two lines are equal, then the lines are parallel.

Step 1: Calculate the slope of Line 1

The formula to calculate the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

For Line 1, the points are $(6, 4)$ and $(20, 12)$: $m_1 = \frac{12 - 4}{20 - 6} = \frac{8}{14} = \frac{4}{7}$

Step 2: Calculate the slope of Line 2

For Line 2, the points are $(2, -3)$ and $(9, 1)$: $m_2 = \frac{1 - (-3)}{9 - 2} = \frac{1 + 3}{9 - 2} = \frac{4}{7}$

Step 3: Compare the slopes

Both Line 1 and Line 2 have the same slope of $\frac{4}{7}$.

Since the slopes are equal, the lines are parallel.

Conclusion:

The correct answer is C. Line 1 is parallel to Line 2 because their slopes are equal to $\frac{4}{7}$.

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Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the situation change if the slopes of the lines were different?
2. What does the slope tell us about the steepness of a line?
3. Can two lines with different slopes ever be parallel?
4. How can we determine if two lines are perpendicular?
5. What does it mean geometrically for two lines to have the same slope?

Tip: Parallel lines always have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.