# Question #f80c7

Nov 6, 2017

If the line is perpendicular, its slope should be $\frac{1}{3}$.

If the line is parallel, the slope should remain the same (ie. $- 3$), but the $y$-intercept should be different.

#### Explanation:

Perpendicular lines have slopes that are the negative reciprocal of each other, and since the slope of

$f \left(x\right) = - 3 x + 6$

is $- 3$ (or $- \frac{3}{1}$, if that helps you visualize it), then the negative reciprocal--aka flipping the number-- would result in $\frac{1}{3}$.

What do parallel lines mean? It means that they'll never touch. If two lines have the same slope but different y-intercepts, they will never touch. Just visualize it.

And, well, if the other line that you didn't specify meets none of the above criteria, then it is neither.

Hope this helps!

Best wishes,
A fellow highschool student.