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

Responses

y=−1/2x+6
y is equal to negative 1 half x plus 6

y=1/2x+3
y is equal to 1 half x plus 3

y=1/2x−5
y is equal to 1 half x minus 5

y=−2x+7

1 answer

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

  1. For the equation \( y = -\frac{1}{2}x + 6 \), the slope is \( -\frac{1}{2} \).
  2. For the equation \( y = \frac{1}{2}x + 3 \), the slope is \( \frac{1}{2} \).
  3. For the equation \( y = \frac{1}{2}x - 5 \), the slope is \( \frac{1}{2} \).
  4. For the equation \( y = -2x + 7 \), the slope is \( -2 \).

Now, we compare the slopes:

  • The first equation has a slope of \( -\frac{1}{2} \).
  • The second and third equations both have a slope of \( \frac{1}{2} \) (these are parallel).
  • The fourth equation has a slope of \( -2 \).

Therefore, the lines that are parallel are:

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