Question

Identify which two lines are parallel.
A: y = 1/2x + 3 and y = 1/2x - 5
B: y = 2/3x -6 and y = -2/3x - 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 evaluate the slopes of each pair:

A:
- \(y = \frac{1}{2}x + 3\) (slope = \(\frac{1}{2}\))
- \(y = \frac{1}{2}x - 5\) (slope = \(\frac{1}{2}\))

Both lines in A have the same slope \( \frac{1}{2} \), so they are parallel.

B:
- \(y = \frac{2}{3}x - 6\) (slope = \(\frac{2}{3}\))
- \(y = -\frac{2}{3}x - 6\) (slope = \(-\frac{2}{3}\))

These lines have different slopes, so they are not parallel.

C:
- \(y = \frac{1}{3}x + 4\) (slope = \(\frac{1}{3}\))
- \(y = \frac{1}{3}x + 4\) (slope = \(\frac{1}{3}\))

Both lines in C have the same slope \( \frac{1}{3} \), so they are parallel.

D:
- \(y = -\frac{1}{2}x + 6\) (slope = \(-\frac{1}{2}\))
- \(y = \frac{1}{2}x - 8\) (slope = \(\frac{1}{2}\))

These lines have different slopes, so they are not parallel.

Final answer: Lines A and C are parallel.

Answer 2

so which answer would it be?

Answer 3

The two lines that are parallel are found in options **A** and **C**.

- **A:** \( y = \frac{1}{2}x + 3 \) and \( y = \frac{1}{2}x - 5 \) (both have a slope of \(\frac{1}{2}\))
- **C:** \( y = \frac{1}{3}x + 4 \) and \( y = \frac{1}{3}x + 4 \) (both have a slope of \(\frac{1}{3}\))

So the answer is:
**A and C are the pairs of parallel lines.**

Answer 4

only one answer is able to be chosen

Answer 5

I apologize for the oversight. If only one answer must be chosen to indicate which pairs of lines are parallel, then:

**The correct answer is A:** \( y = \frac{1}{2}x + 3 \) and \( y = \frac{1}{2}x - 5 \).

These two lines are parallel because they both have the same slope of \(\frac{1}{2}\).