

y=4x+2
y=−14x+5
y=4x+9
y+4=−14(x−3)
y=−4x+6
y−4=4(x+3)
y=14x+8
y=−14x+9
The equation of line A
 is y=4x−3
 .

Sort the following equations of lines as parallel or perpendicular to line A
. Not all equations will be used.
 
Parallel to Line A
Perpendicular to Line A
 

To determine which lines are parallel or perpendicular to line A, we need to compare their slopes.

**Line A equation:** \( y = 4x - 3 \)

- The slope of line A is **4**.

**For parallel lines:**
- Lines with the same slope as line A (i.e., slope = 4) are parallel.

**For perpendicular lines:**
- Lines whose slopes are the negative reciprocal of the slope of line A (i.e., slope = -1/4) are perpendicular.

Now, let's identify the slope of each equation:

1. **\( y = 4x + 2 \)**  
   - Slope = 4  
   **Parallel to line A**

2. **\( y = -14x + 5 \)**  
   - Slope = -14  
   Neither parallel nor perpendicular

3. **\( y = 4x + 9 \)**  
   - Slope = 4  
   **Parallel to line A**

4. **\( y + 4 = -14(x - 3) \)**  
   - Rewrite as: \( y = -14x + 38 \)  
   - Slope = -14  
   Neither parallel nor perpendicular

5. **\( y = -4x + 6 \)**  
   - Slope = -4  
   Neither parallel nor perpendicular

6. **\( y - 4 = 4(x + 3) \)**  
   - Rewrite as: \( y = 4x + 16 \)  
   - Slope = 4  
   **Parallel to line A**

7. **\( y = 14x + 8 \)**  
   - Slope = 14  
   Neither parallel nor perpendicular

8. **\( y = -14x + 9 \)**  
   - Slope = -14  
   Neither parallel nor perpendicular

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### Summary:

**Parallel to Line A:**
- \( y = 4x + 2 \)
- \( y = 4x + 9 \)
- \( y - 4 = 4(x + 3) \)

**Perpendicular to Line A:**
- None of the equations have a slope of -1/4, so **no perpendicular lines**.

Would you like more details or have any questions?

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Here are five related questions to expand on this topic:
1. How do you determine the slope of a line from an equation?
2. Can two lines with different y-intercepts be parallel?
3. What is the geometric relationship between parallel and perpendicular lines?
4. How can we transform a given equation into slope-intercept form \( y = mx + b \)?
5. What are other methods to check if two lines are perpendicular?

**Tip:** Always rewrite equations into slope-intercept form \( y = mx + b \) to easily identify the slope.

Sort the following equations of lines as parallel or perpendicular to line A. Not all equations will be used.

Learn how to classify lines as parallel or perpendicular to Line A (y = 4x - 3). This problem uses algebraic concepts like slopes, parallel lines, and perpendicular lines, suitable for students in Grades 8-10.

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