The equations of five lines are given below. Line A=y=2x+3 Line B=1/2x-3 Line C=y=6-x Line D y-2x=7 Line E y+2x=3 Which two lines are parallel?


To determine which two lines are parallel, we need to compare the **slopes** of the lines. Parallel lines have the **same slope** but different y-intercepts.

Let's analyze the equations and their slopes:

- **Line A: \( y = 2x + 3 \)**  
  The slope is \( 2 \).

- **Line B: \( y = \frac{1}{2}x - 3 \)**  
  The slope is \( \frac{1}{2} \).

- **Line C: \( y = 6 - x \)**  
  Rewrite as \( y = -x + 6 \).  
  The slope is \( -1 \).

- **Line D: \( y - 2x = 7 \)**  
  Rewrite as \( y = 2x + 7 \).  
  The slope is \( 2 \).

- **Line E: \( y + 2x = 3 \)**  
  Rewrite as \( y = -2x + 3 \).  
  The slope is \( -2 \).

### Conclusion:
Lines **A** and **D** are parallel because both have the same slope of \( 2 \).

Would you like any details or have any further questions?

Here are 5 related questions:

1. What happens when two lines have the same slope but different y-intercepts?
2. How do you determine if two lines are perpendicular?
3. Can lines with the same y-intercept ever be parallel?
4. How can you find the distance between two parallel lines?
5. How do you determine the slope from two points on a line?

**Tip:** Parallel lines always have equal slopes but different y-intercepts. If the y-intercepts are the same, the lines overlap.

Explore how to identify parallel lines by analyzing their slopes. Understand the concept of parallel lines in geometry with examples of equations and their slopes. Suitable for students in Grades 7-9.

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