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In the provided graph, the question asks whether lines \( L_1 \) and \( L_2 \) are parallel, and the correct answer is highlighted as option **A**, which states: 

*Yes, lines \( L_1 \) and \( L_2 \) are parallel because they have the same slope.*

### Explanation:
For two lines to be parallel, they must have the same slope. Let's determine the slopes of the two lines by using the coordinates provided.

- For \( L_1 \), we can see two points: \( (0, 2) \) and \( (6, 6) \).
  - The slope of a line is given by:
    \[
    m = \frac{y_2 - y_1}{x_2 - x_1}
    \]
    Substituting the points \( (0, 2) \) and \( (6, 6) \):
    \[
    m_1 = \frac{6 - 2}{6 - 0} = \frac{4}{6} = \frac{2}{3}
    \]

- For \( L_2 \), the points are \( (0, -3) \) and \( (6, -6) \).
  - Using the same formula for slope:
    \[
    m_2 = \frac{-6 - (-3)}{6 - 0} = \frac{-6 + 3}{6} = \frac{-3}{6} = -\frac{1}{2}
    \]

Thus, the two slopes are \( \frac{2}{3} \) for \( L_1 \) and \( -\frac{1}{2} \) for \( L_2 \).

Since the slopes are **not equal**, **lines \( L_1 \) and \( L_2 \) are not parallel**. Therefore, the correct answer should actually be **D: No, lines \( L_1 \) and \( L_2 \) are not parallel because they have different slopes**.

Would you like further details or have any questions on this? 

Here are 5 related questions to expand on this:

1. How do you calculate the slope of a line between two points?
2. What conditions are required for two lines to be perpendicular?
3. What is the equation of a line if you know its slope and a point on the line?
4. How would you determine if two lines intersect?
5. How can parallel and perpendicular lines be applied in real-life geometry problems?

**Tip:** Always compare the slopes of two lines to determine if they are parallel. If the slopes are equal, the lines are parallel; if they are negative reciprocals, the lines are perpendicular.

In the graph to the right, are lines L₁ and L₂ parallel? Explain.

Learn how to determine if two lines are parallel using their slopes. This example uses a graph with lines L₁ and L₂ and explores the calculation of their slopes using the formula m = (y₂ - y₁) / (x₂ - x₁). Suitable for students in Grades 8-10.

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