To determine if John’s claim is correct, we need to calculate the slopes of both lines. Two lines are parallel if and only if their slopes are equal.

Step 1: Find the slope of Line 1

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

Step 2: Find the slope of Line 2

Line 2 passes through the points $(2, -3)$ and $(9, 1)$. Using the same formula for the slope:

$m_2 = \frac{1 - (-3)}{9 - 2} = \frac{1 + 3}{9 - 2} = \frac{4}{7}$

Step 3: Compare the slopes

Both Line 1 and Line 2 have the same slope of $\frac{4}{7}$. Since their slopes are equal, the lines are parallel.

Conclusion:

John's claim is correct. The correct reason is that their slopes are both $\frac{4}{7}$, which simplifies to option C.

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

Would you like more details or have any questions?

Related questions:

1. How do you find the equation of a line given two points?
2. What are the conditions for two lines to be perpendicular?
3. What happens if two lines have the same slope but different y-intercepts?
4. How can you determine if two lines are skew instead of parallel?
5. What is the geometric interpretation of the slope?

Tip: Always remember that parallel lines have identical slopes, but different y-intercepts!