Are the lines with equations 2x + y = 2 and x - 2y = 0 parallel, perpendicular or neither?

Expert Answers

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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.

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