In this problem, you are asked if lines $L_1$ and $L_2$ in the graph are parallel based on their slopes. The correct answer, as highlighted in the image, is:

• No, lines $L_1$ and $L_2$ are not parallel because they have different slopes.

Explanation:

To determine if two lines are parallel, their slopes must be identical. Let's compute the slopes of the two lines to verify this.

• Line $L_1$:

  • Using the points $(-8, -3)$ and $(0, -5)$, the slope $m$ is calculated by: $m_1 = \frac{-5 - (-3)}{0 - (-8)} = \frac{-5 + 3}{0 + 8} = \frac{-2}{8} = -\frac{1}{4}$

• Line $L_2$:

  • Using the points $(0, 1)$ and $(9, 12)$, the slope $m$ is calculated by: $m_2 = \frac{12 - 1}{9 - 0} = \frac{11}{9}$

Since the slopes $m_1 = -\frac{1}{4}$ and $m_2 = \frac{11}{9}$ are different, the lines are not parallel. Therefore, the answer is correctly marked as:

Option A: No, lines $L_1$ and $L_2$ are not parallel because they have different slopes.

Do you want more details or have any questions?

Here are some related questions for further practice:

1. What does it mean for two lines to be perpendicular in terms of their slopes?
2. How would you find the slope of a line from its equation in slope-intercept form?
3. Can two lines with different slopes ever intersect at more than one point?
4. If two lines have the same slope but different y-intercepts, are they always parallel?
5. How would you find the equation of a line parallel to a given line passing through a specific point?

Tip: When calculating slopes, remember to keep track of signs, as this determines the direction of the line.