# Question #e4d90

Feb 20, 2017

It's all a matter of understanding the relation between the slopes of these lines. Answers below...

#### Explanation:

Two lines, written in slope-intercept form are parallel if they have the same slope.

So, a line parallel to $y = \frac{1}{6} x + 1$ would be $y = \frac{1}{6} x + b$ where $b$ can be any value (the $y$-intercept of the line) other than 1.

A line is perpendicular to another if its slope is the negative reciprocal of the other line.

In this case, the perpendicular line would have a slope of -6, since the given line has slope $\frac{1}{6}$.

It's equation could be $y = - 6 x + b$, where again, $b$ could be any value you wish (including 1 this time).