Question

Identify which two lines are parallel.
(1 point)
Y=-1/2x+6a and y =1/2x -8
Y=1/2x +3 and y = 1/2x -5
Y=2/3x -6 and y = -3/2x -6
Y=1/3x +4 and y =1/3x +4

Answer 1

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:

1. \( y = -\frac{1}{2}x + 6a \) (slope = -1/2) and \( y = \frac{1}{2}x - 8 \) (slope = 1/2)
- These lines have different slopes, so they are not parallel.

2. \( y = \frac{1}{2}x + 3 \) (slope = 1/2) and \( y = \frac{1}{2}x - 5 \) (slope = 1/2)
- These lines have the same slope, so they are parallel.

3. \( y = \frac{2}{3}x - 6 \) (slope = 2/3) and \( y = -\frac{3}{2}x - 6 \) (slope = -3/2)
- These lines have different slopes, so they are not parallel.

4. \( y = \frac{1}{3}x + 4 \) (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.