Question

Which of the lines listed below are parallel? (PICK TWO)(1 point)
Responses

y=−12x+6
y is equal to negative 1 half x plus 6

y=12x+3
y is equal to 1 half x plus 3

y=12x−5
y is equal to 1 half x minus 5

y=−2x+7

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 rewrite the equations in slope-intercept form \(y = mx + b\), where \(m\) is the slope:

1. \(y = -12x + 6\) (slope = -12)
2. \(y = -\frac{1}{2}x + 6\) (slope = -\frac{1}{2})
3. \(y = 12x + 3\) (slope = 12)
4. \(y = \frac{1}{2}x + 3\) (slope = \frac{1}{2})
5. \(y = 12x - 5\) (slope = 12)
6. \(y = \frac{1}{2}x - 5\) (slope = \frac{1}{2})
7. \(y = -2x + 7\) (slope = -2)

Now, we'll compare the slopes:

- Lines with slope 12: \(y = 12x + 3\) and \(y = 12x - 5\) are parallel.
- Lines with slope \(\frac{1}{2}\): \(y = \frac{1}{2}x + 3\) and \(y = \frac{1}{2}x - 5\) are parallel.

So, the two pairs of parallel lines are:
- \(y = 12x + 3\) and \(y = 12x - 5\)
- \(y = \frac{1}{2}x + 3\) and \(y = \frac{1}{2}x - 5\)

Thus, the lines that are parallel are \(y=12x+3\) and \(y=12x−5\) (these are one pair), or potentially another valid selection could be any of the \(\frac{1}{2}\) slope lines.