https://file.aiquickdraw.com/mathbot/file/1729285532661j7avmb0u.jpg

To determine whether the graphs of the given equations are parallel, perpendicular, or neither, let's first analyze the two equations:

1. \( y = x + 10 \)
2. \( y = -x + 2 \)

### Step 1: Compare the slopes
The general form of a linear equation is \( y = mx + b \), where \( m \) represents the slope of the line.

- For the first equation \( y = x + 10 \), the slope is \( m_1 = 1 \).
- For the second equation \( y = -x + 2 \), the slope is \( m_2 = -1 \).

### Step 2: Determine the relationship between the slopes
- **Parallel lines** have the same slope, meaning \( m_1 = m_2 \).
- **Perpendicular lines** have slopes that are negative reciprocals of each other, meaning \( m_1 \cdot m_2 = -1 \).

Now, multiplying the slopes of these lines:
\[
m_1 \cdot m_2 = 1 \cdot (-1) = -1
\]
Since the product of the slopes is \( -1 \), the lines are **perpendicular**.

### Final Answer: The correct answer is **Perpendicular**.

Would you like further explanation or details?

Here are five related questions to expand on this:
1. How can you identify parallel lines using their equations?
2. What are the conditions for two lines to be perpendicular?
3. Can two lines be both parallel and perpendicular at the same time? Why or why not?
4. How does the slope-intercept form help in graphing linear equations?
5. What happens when the slopes of two lines are neither equal nor negative reciprocals?

**Tip:** Always compare slopes first when determining relationships between lines (parallel, perpendicular, or neither).

Determine whether the graphs of the given equations are parallel, perpendicular, or neither. 
1. y = x + 10 
2. y = -x + 2

Learn how to determine if two lines are parallel, perpendicular, or neither by analyzing the slopes of the equations y = x + 10 and y = -x + 2. This problem involves the slope-intercept form and the relationships between the slopes of two lines. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation