Question

Identify which two lines are parallel.(1 point)
Responses

y=23x−6
and y=−32x−6
y equals two-thirds x minus 6 and y equals negative three-halves x minus 6

y=12x+3
and y=12x−5
y equals Start Fraction 1 over 2 End Fraction x plus 3 and y equals Start Fraction 1 over 2 End Fraction x minus 5

y=13x+4
and y=13x+4
y equals Start Fraction 1 over 3 End Fraction x plus 4 and y equals Start Fraction 1 over 3 End Fraction x plus 4

y=−12x+6
and y=12x−8

Answer 1

To determine which two lines are parallel, we need to look for lines that have the same slope (the coefficient of x).

Here's the list of the equations:

1. \(y = 23x - 6\) and \(y = -32x - 6\)
- Slopes: 23 and -32 (not parallel)

2. \(y = \frac{2}{3}x - 6\) and \(y = -\frac{3}{2}x - 6\)
- Slopes: \(\frac{2}{3}\) and \(-\frac{3}{2}\) (not parallel)

3. \(y = 12x + 3\) and \(y = 12x - 5\)
- Slopes: 12 and 12 (parallel)

4. \(y = \frac{1}{2}x + 3\) and \(y = \frac{1}{2}x - 5\)
- Slopes: \(\frac{1}{2}\) and \(\frac{1}{2}\) (parallel)

5. \(y = -12x + 6\) and \(y = 12x - 8\)
- Slopes: -12 and 12 (not parallel)

The lines that are parallel are:

- \(y = 12x + 3\) and \(y = 12x - 5\)
- \(y = \frac{1}{2}x + 3\) and \(y = \frac{1}{2}x - 5\)

Thus, the response containing the following two lines is the answer:

**y = 12x + 3 and y = 12x - 5** (they have the same slope of 12).