Let's analyze the graph and solve the question.

Step 1: Find the slopes of both lines.

The two lines cross at the origin $(0, 0)$. Let's use the slope formula to calculate their slopes. The slope $m$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Line 1: Positive Slope Line (from bottom-left to top-right)

This line passes through points $(-10, -10)$ and $(10, 10)$. $m_1 = \frac{10 - (-10)}{10 - (-10)} = \frac{20}{20} = 1$

Line 2: Negative Slope Line (from top-left to bottom-right)

This line passes through points $(-10, 10)$ and $(10, -10)$. $m_2 = \frac{-10 - 10}{10 - (-10)} = \frac{-20}{20} = -1$

Step 2: Determine the relationship between the slopes.

• The slopes of the two lines are $1$ and $-1$.
• If the product of two slopes is $-1$, the lines are perpendicular.

$1 \times (-1) = -1$ Thus, the two lines are perpendicular.

Answer:

The correct option is: A. The lines are perpendicular to each other.

Do you want further explanation?

Here are 5 related questions you might find useful:

1. How do you determine if two lines are parallel using their slopes?
2. What is the equation of a line given a point and a slope?
3. How do you find the intersection point of two lines?
4. What is the general form of the equation of a line in slope-intercept form?
5. What are coinciding lines, and how do they relate to slope?

Tip: Perpendicular lines always have slopes that multiply to $-1$.