Maths: Perpendicular Lines?

Question

Hello, thanks for any help :)!

I have a maths problem, in the chapter The Equation of a Straight Line in the form of y - b = m (x-a) and perpendicular lines.

The Question is;

"Is this pair of lines perpendicular to each other;

3x - y - 2 = 0 and 3y + x + 7 = 0"

When I try to rearrange the first equation into the form of 'y =' I ended up getting - y = -3x + 2.

So, when I do the equation m1 x m2 = -1 to prove that these are perpendicular to each other, I end up getting 1 instead of -1. However, I looked at the answers and it says they are perpendicular.

Answer 1

y = 3x - 2 is the first one.

3y + x + 7 = 0

x + 7 = -3y  (subtract 3y from both sides)

(-1/3)x - (7/3) = y  (divide out by -3)

therefore they are perpendicular because they're slopes are 3 and -1/3. they are negative reciprocals

(3)(-1/3) = -1

RESPONSE TO FOLLOW -UP

just add y to both sides

Answer 2

You didn't finish rearranging the first equation. You left is at -y, when your suppose to have y. To fix that, you just need to multiply -1 to everything.

-1[- y = -3x + 2]

y = 3x - 2

The equation for the other line should look like:

y = (-1/3)x - 7/3

so, when you multiply the two slopes together, you should get -1 now.



3 * (-1/3) = -1

I hope that helps!