To identify which two lines are parallel, we need to look for lines that have the same slope. The slope-intercept form of a linear equation is \( y = mx + b \), where \( m \) is the slope.
Now let's analyze the given lines:
-
\( y = -\frac{1}{2}x + 6a \) (slope = -1/2) and \( y = \frac{1}{2}x - 8 \) (slope = 1/2)
- These lines have different slopes, so they are not parallel.
-
\( y = \frac{1}{2}x + 3 \) (slope = 1/2) and \( y = \frac{1}{2}x - 5 \) (slope = 1/2)
- These lines have the same slope, so they are parallel.
-
\( y = \frac{2}{3}x - 6 \) (slope = 2/3) and \( y = -\frac{3}{2}x - 6 \) (slope = -3/2)
- These lines have different slopes, so they are not parallel.
-
\( y = \frac{1}{3}x + 4 \) (slope = 1/3) and \( y = \frac{1}{3}x + 4 \) (slope = 1/3)
- These lines have the same slope, so they are parallel.
The two pairs of lines that are parallel are:
- \( y = \frac{1}{2}x + 3 \) and \( y = \frac{1}{2}x - 5 \)
- \( y = \frac{1}{3}x + 4 \) and \( y = \frac{1}{3}x + 4 \)
However, since you only wanted to identify one set, the first valid pair you mentioned is sufficient:
- \( y = \frac{1}{2}x + 3 \) and \( y = \frac{1}{2}x - 5 \) are parallel.