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.