# How do you tell whether the lines for each pair of equations are parallel, perpendicular, or neither: y=(-1/5)x+6, -2x+10y=5?

Dec 11, 2016

They are neither parallel nor perpendicular.

#### Explanation:

Given -

$y = \left(- \frac{1}{5}\right) x + 6$ -------------------------(1)
$- 2 x + 10 y = 5$---------------------------(2)

The first line equation is in the slope intercept form

$y = m x + c$

The slope ${m}_{1}$ of the 1st line is $= - \frac{1}{5}$

The second line is in the form

$a x + b y = c$

In this case, slope is defined by $- \frac{a}{b}$

Applying this formula, the slope ${m}_{2}$ of the second line $= - \frac{- 2}{10} = \frac{1}{5}$

Then apply these conditions to decide the types of relation between the two lines.

If ${m}_{1} = {m}_{2}$, then the two lines are parallel to each other.
If the product of ${m}_{1}$ and ${m}_{2}$ is equal to $- 1$ , then the two lines are perpendicular to each other.

Otherwise, the two lines are neither parallel nor perpendicular.

In our case ${m}_{1} = - \frac{1}{5}$ and ${m}_{2} = \frac{1}{5}$ satisfy neither of the two conditions.

Hence they are neither parallel nor perpendicular.