Question

Without graphing, tell whether each pair of lines is parallel, perpendicular, or neither.

Answer 1

(i) Given:

`x=2,y=-5`

These two lines are straight lines and perpendicular to each other.

(ii) Given:

`\begin{gathered} y=7x \\ y-28=7(x-4) \end{gathered}`

Since the slope of both equations is the same (m=7).

Hence, the lines are parallel.

(iii) Given:

`\begin{gathered} y=2x-1 \\ y=(1)/(2)x+2 \end{gathered}`

The slope of the first equation is 2.

The slope of the second equation is 1/2.

Since they are neither parallel nor perpendicular.

Hence, the answer is neither.

(iv)Given:

`\begin{gathered} y-3=(1)/(4)(x-3) \\ y+13=(1)/(4)(x+1) \end{gathered}`

Since the slope of both equations is the same.

That is,

`m=(1)/(4)`

Hence, the lines are parallel.