Question

The equations of two lines are x - 3y = 6 and y = 3x + 2. Determine if the lines are parallel, perpendicular or neither, i dont know how to find out if its parallel or perpendicular

Answer 1

what's the slope of the 2nd one? that is y = 3x + 2.

Answer 2

3x

Answer 3

hmm have you covered slopes yet?

Answer 4

yes, im just having a bit of a hard time with it

Answer 5

hmmm anyhow.... the slope would be 3 only without the "x"

so the idea being..

parallel - they both have the same exact slope
perpendicular - the slope of one, is the same as the other BUT upside down and negative

neither - see above =)

so... the let us see their slopes then \(bf x-3y=6\implies -3y=-x+6\implies y=\cfrac{-x+6}{-3}\implies y=\cfrac{x}{-3}+\cfrac{\cancel{ 6 }}{\cancel{ -3 }}
\\ \quad \\
y={\color{brown}{ -\cfrac{1}{3}}}x+2\)

and the slope of the 2nd one is \(\bf y = {\color{brown}{ 3}}x + 2\)


now, look at the slopes..... what do you think? paralle, perpendicular or neither?

Answer 6

neither?

Answer 7

hmm what makes you think they're not parallel? or perpendicular?

Answer 8

the slopes arent the same and they arent negative

Answer 9

but the y intercepts are the same

Answer 10

hmm notice the "dash" in front of the 1st slope, that one is negative

Answer 11

so they're not the same..... true

but is one the same as the other upside down and negative?

Answer 12

OOOOOOOHHHH!!!! I GET IT

Answer 13

keep in mind that anynumber is the same as anynumber/1
that is \(\bf 5=\cfrac{5}{1}\qquad 1,000=\cfrac{1,000}{1}\) and so on

Answer 14

okay, thank you so much for your help :3

Answer 15

\(\bf x-3y=6\implies -3y=-x+6\implies y=\cfrac{-x+6}{-3}\implies y=\cfrac{x}{-3}+\cfrac{\cancel{ 6 }}{\cancel{ -3 }}
\\ \quad \\
y={\color{brown}{ -\cfrac{1}{3}}}x+2
\\ \quad \\ \quad \\
y = {\color{brown}{ 3}}x + 2\implies y = {\color{brown}{ \cfrac{+3}{1}}}x + 2\)

Answer 16

yw