To determine which pair of lines are parallel, we need to analyze the equations and their slopes.

The general form of a linear equation is $y = mx + b$, where:

• $m$ is the slope of the line.
• $b$ is the y-intercept.

Step 1: Rewrite each equation to match the slope-intercept form ($y = mx + b$):

1. $y = 2 + \frac{x}{2}$

   • This can be rewritten as $y = \frac{1}{2}x + 2$, so the slope is $m = \frac{1}{2}$.

2. $y = \frac{x}{2} + 4$

   • This is already in slope-intercept form: $y = \frac{1}{2}x + 4$, so the slope is $m = \frac{1}{2}$.

3. $y = 8 - \frac{x}{2}$

   • This can be rewritten as $y = -\frac{1}{2}x + 8$, so the slope is $m = -\frac{1}{2}$.

4. $y = \frac{1}{2}(5 - 2x)$

   • First, distribute the $\frac{1}{2}$: $y = \frac{1}{2}(5) - \frac{1}{2}(2x) = \frac{5}{2} - x$.
   • Rewriting it: $y = -x + \frac{5}{2}$, so the slope is $m = -1$.

Step 2: Compare the slopes:

• Equations 1 and 2 both have the slope $m = \frac{1}{2}$.
• Equations 3 and 4 have different slopes.

Conclusion: The pair of parallel lines is:

• $y = 2 + \frac{x}{2}$ and $y = \frac{x}{2} + 4$.

Would you like further details or have any questions?

Here are 5 related questions:

1. What makes two lines parallel in terms of their slopes?
2. How do you find the slope from an equation in slope-intercept form?
3. How would you convert a more complex linear equation to slope-intercept form?
4. Can two lines with different y-intercepts but the same slope still be parallel?
5. What happens to the slope if the coefficient of $x$ is negative?

Tip: When analyzing equations for parallelism, always focus on the slopes. Parallel lines always have identical slopes.