Question

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

Answer 1

For parallel lines, they have the same slope
For perpendicular lines, the product of their slopes = -1
If they do not satisfy both condition, they are the 'neither' case :)
So can you work out the slopes first?

Answer 2

no i'm really struggling with this whole thing :/

Answer 3

first change to the slope-intercept form

the first is already in the form...y = 3x/8 + 6

the second...
6y = -16x -16
y = -16/6 x - 16/6
y = -8/3 x - 8/3

so the slope of the first is 3/8
the slope of the second is -8/3

what do you think they are? parallel? perpendicular? or neither?

Answer 4

y = 3x/8 +6

16x +6y = -16
(rearranging into y=mx+b form)

6y = -16x -16
y= -16x/6 -16/6

y = -8x/3 -16

Now ALL we have to do is look at the slopes of each of these. If the slopes are the same, then they are parallel. If they one is the negative inverse of the other, then it's perpendicular.

For example, if m=4/5, then the slope perpendicular to this would be: m=-5/4

If it's neither of these, then it's neither.

y = 3x/8 +6
y = -8x/3 -16

Look at the slopes of these two. And remember, it always important to get your line eqn in the y=mx+b format.

Answer 5

Forgot to erase "they," sorry to sound like an idiot lol.

Answer 6

eqn 1: m = 3/8
eqn 2: m = -8/3

So: What do you think? Par, Perp, neither?

Answer 7

i'm thinking neither but not really sure. i know its not parallel

Answer 8

As long as you know they are not //, you can try multiplying them, what would you get for the product of the 2 slopes?

Answer 9

Well -8/3 is the negative inverse of 3/8.

If a slope is the negative inverse of another slope, then that means they're perpendicular.


If you have m=3, then the perpendicular slope would be -1/3.

If you have m=-3/2, then the perpendicular slope would be 2/3.

All I did with those two examples was flipped the number and added on a negative sign.

Answer 10

Is this clicking for you now?