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 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.

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

Learn how to determine if two lines are parallel by calculating their slopes. This problem involves finding the slopes of Line 1 and Line 2 using the slope formula and verifying if they are equal. Suitable for students in Grades 8-10 studying geometry and linear equations.

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