John claims that the two lines described below are parallel.
 
Line 1
 passes through points (6, 4)
 and (20,12)
.
Line 2
 passes through points (2,−3)
 and (9, 1)
.

Which of the following reasons support his claim?
A.Line 1
 is parallel to Line 2
 because their slopes are equal to −47

B.Line 1
 is parallel to Line 2
 because their slopes are equal to −74

C.Line 1
 is parallel to Line 2
 because their slopes are equal to 47

D.Line 1
 is parallel to Line 2
 because their slopes are equal to 74


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!

John claims that the two lines described below are parallel. Line 1 passes through points (6, 4) and (20, 12). Line 2 passes through points (2,−3) and (9, 1). Which of the following reasons support his claim? A. Line 1 is parallel to Line 2 because their slopes are equal to −47 B. Line 1 is parallel to Line 2 because their slopes are equal to −74 C. Line 1 is parallel to Line 2 because their slopes are equal to 47 D. Line 1 is parallel to Line 2 because their slopes are equal to 74

Explore how to determine if two lines are parallel by calculating their slopes. This problem focuses on using the slope formula to show that Line 1 and Line 2 are parallel with equal slopes of 4/7. Suitable for students in Grades 8-10.

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