Question

Determine whether these lines are parallel, perpendicular, or neither.

y = -1/2 x + 1
y = 2x +1

Answer 1

hint: parallel lines have the same slope value
perpendicular ones, have a NEGATIVE RECIPROCAL slope value
\(\bf slope=\cfrac{a}{{\color{blue}{ b}}}\qquad negative\implies -\cfrac{a}{{\color{blue}{ b}}}\qquad reciprocal\implies - \cfrac{{\color{blue}{ b}}}{a}\)

Answer 2

If they are parallel, they would have the same gradient.

If they are perpendicular, gradient of one of them would be -1 divided by gradiend of the other. (Refer to jdoe's image above)

Answer 3

The slopes are - 1/2 and 2 so would it be neither

Answer 4

Or perpendicular?

Answer 5

Lets look at the second equation. Its gradient is 2. Lets say m1 = 2

If the other line is perpendicular, its gradient(m2) would be:
m2 = -1/m1

Answer 6

So it's perpendicular, right?

Answer 7

m2 = -1/2

Yes, it would be perpendicular.

Answer 8

Here is another example for future references:

Answer 9

oh, okay. Thank you!