Question

Are the pair of lines y = 1/2x + 1 and y = -1/2x +2 parallel, perpendicular, or neither?

Answer 1

It is given that

`y=(1)/(2)x+1\ldots\text{.}\mathrm{}(1)`

`y=-(1)/(2)x+2\ldots\text{.}(1)`

The general form of the line equation is

`y=mx+c\ldots\ldots(3)`

Here m is the slope of the line.

Comparing equation (1) and equation (3), we get

The slope of the first line is

`m_1=(1)/(2)`

Comparing equation (2) and equation (3), we get

The slope of the second line is

`m_2=-(1)/(2)`

Here

`m_1=(1)/(2)\\e-(1)/(2)=m_2`

These two lines are not parallel

The perpendicular condition is

`m_1=-(1)/(m_2)`

Substitute values, we get

`(1)/(2)=-(1)/(-(1)/(2))`

`(1)/(2)=-(1)/(1)*-(2)/(1)`

`(1)/(2)=2`

This is not true.

Hence these two lines are not perpenticular.

The given pair of lines are neither parallel nor perpendicular.