# Consider the line x- 8y =2. What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line?

Dec 30, 2016

Slope of line perpendicular to $y$ is $- 8$
Slope of line parallel to $y$ is $\frac{1}{8}$

#### Explanation:

$x - 8 y = 2 \to y = \frac{x}{8} - \frac{1}{4}$

The slope of a straight line in slope $\left(m\right)$ and intercept $\left(c\right)$ form is:
$y = m x + c$

$\therefore$ In this example, the slope of the line $y$ is: $\frac{1}{8}$

If two lines of slopes ${m}_{1}$ and ${m}_{2}$ are perpendicular to eachother, then: ${m}_{1} \times {m}_{2} = - 1$

Hence the slope $\left({m}_{2}\right)$ of the line perpendicular to $y$ will have a slope of: $- \frac{1}{\frac{1}{8}} = - 8$

Any line parallel to $y$ will have the same slope $\left({m}_{1}\right)$ as $y$

Hence, a line parallel to $y$ has a slope of $\frac{1}{8}$