Question

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`?

Answer 1

They are neither parallel nor perpendicular.

Explanation:

Given -

`y=(-1/5)x+6` -------------------------(1)
`-2x+10y=5`---------------------------(2)

The first line equation is in the slope intercept form

`y=mx+c`

The slope `m_1` of the 1st line is `=-1/5`

The second line is in the form

`ax+by=c`

In this case, slope is defined by `-a/b`

Applying this formula, the slope `m_2` of the second line `=-(-2)/10=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=-1/5` and `m_2=1/5` satisfy neither of the two conditions.

Hence they are neither parallel nor perpendicular.