Show that the straight lines x + 2y + 1 = 0 and 3x + 6y + 2 = 0 are parallel.

Given: Here the straight lines are x + 2y + 1 = 0 and

3x + 6y + 2 = 0.

To Prove: x + 2y + 1 = 0 and 3x + 6y + 2 = 0 are parallel.

Proof: If two lines are parallel then their slopes are equal.

Here slope of the first line x + 2y + 1 = 0 will be

(When the line is in the form ax + by + c = 0 then the slope of the line is )

⇒

Here slope of the second line 3x + 6y + 2 = 0 will be

⇒

⇒

Now both the slopes are equal.

Hence both the lines are parallel.