To know whether two lines are parallel, you must see if the slops of the equations which correspond to the two lines are the same.
Concerning, perpendicular lines, the product ( multiplication) of their slope will give -1.
Ex 54 :
y = -1/3x and y = -1/3-6 are parallel because they have the same slope "-1/3".
Ex 55 :
y - 2 = -4(x-1)
i.e y = -4x + 6
Therefore : y - 2 = -4(x-1) and y = -4x - 2 are parallel.
Ex 56 :
-5 * 1/5 = -5/5 = -1.
So, y - 1 = -5(x-6) and y = 1/5x + 2 are perpendicular.
Ex 57 :
3 * -1/3 = -3/3 = -1.
Therefore, y - 2 = 3(x+1) and y = -1/3x are perpendicular.
Hope this helps !
Photon
