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.