https://file.aiquickdraw.com/mathbot/file/17301476632391x2i0xxj.jpg

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.**

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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 \(-1\).

After learning about the slopes of parallel and perpendicular lines, answer the question about the lines on the graph. Which statement is true about the lines?
A. The lines are perpendicular to each other.
B. The lines are parallel to each other.
C. The lines are neither parallel nor perpendicular.
D. The lines are coinciding.

Learn how to determine if lines are parallel, perpendicular, or coinciding based on their slopes. This question involves calculating slopes and understanding relationships between them in coordinate geometry. Ideal for students in Grades 8-10.

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