Question

Identify which two lines are parallel.

A. y=1/2x+3 and y=1/2x−5
B. y=2/3x−6 and y=−3/2x−6
C. y=1/3x+4 and y=1/3x+4
D. y=−1/2x+6 and y=1/2x−8

Answer 1

To determine which lines are parallel, we need to look at their slopes. Lines are parallel if they have the same slope.

Let's analyze the lines one by one:

A. \( y = \frac{1}{2}x + 3 \) and \( y = \frac{1}{2}x - 5 \)
- Both lines have a slope of \( \frac{1}{2} \). Therefore, these lines are parallel.

B. \( y = \frac{2}{3}x - 6 \) and \( y = -\frac{3}{2}x - 6 \)
- The slopes are \( \frac{2}{3} \) and \( -\frac{3}{2} \), which are not equal. So, these lines are not parallel.

C. \( y = \frac{1}{3}x + 4 \) and \( y = \frac{1}{3}x + 4 \)
- Both lines are identical, with a slope of \( \frac{1}{3} \). Therefore, these lines are also parallel.

D. \( y = -\frac{1}{2}x + 6 \) and \( y = \frac{1}{2}x - 8 \)
- The slopes are \( -\frac{1}{2} \) and \( \frac{1}{2} \), which are not equal. So, these lines are not parallel.

In conclusion, the two lines that are parallel are:

- **A**: \( y = \frac{1}{2}x + 3 \) and \( y = \frac{1}{2}x - 5 \)
- **C**: \( y = \frac{1}{3}x + 4 \) and \( y = \frac{1}{3}x + 4 \) (they are identical, thus parallel).

Answer 2

You can only pick one