2x + y = 2
x - 2y = 0
First we will rewrite the equation in the slope format:
==> 2x + y = 2
==> y= -2x + 2
Then, the slope m1 = -2
Now we will write equation (2):
x - 2y = 0
Add 2y to both sides.
==> 2y = x
Now we will divide by 2.
==> y= (1/2) x
==> Then, the slope m2 = (1/2)
Now since m1 and m2 are different, then the lines are NOT parallel.
If the lines are perpendicular, then we know that m1*m2 = -1
==> -2 * 1/2 = -1
Then, the lines are perpendicular.