Question

Determine whether the lines are parallel, perpendicular, or neither.
3x - 6y = -1
18x + 9y = 7

Answer 1

You have to rearrange each equation into lope-intercept form and check their slopes. Slope intercept form means you have to get each equation to look like:
\[y=mx+b\]
Where y must be positive and by itself and the number attached to x is the slope. Do you think you would be able to rearrange the equations to look like that form?

Answer 2

no i tried and i just cant get it

Answer 3

Alright, well let's look at the first one 3x-6y = -1. So we need y positive and by itself. So what do you think we should do first to get y by itself?

Answer 4

minus 3x

Answer 5

Alright, cool. So that gives us:
\[-6y = -3x-1\]So now what?

Answer 6

divide 6?

Answer 7

Negative 6 :3. Now let's be careful, we need to divide all 3 terms by -6 and be careful with signs. So we have:
\[\frac{ -6y }{ -6 }=\frac{ -3x }{ -6 }-\frac{ 1 }{ -6 }\]
So the negative 6 on the left goes away. Everything on the right becomes positive And we can simplify the fraction with x to get:
\[y = \frac{ 1 }{ 2 }x+\frac{ 1 }{ 6 }\]So the slope of this line is 1/2, because it is the number paired with x. Understand how I got that?

Answer 8

yes

Answer 9

Alright, good. So now we do the same thing with the second equation and see what its slope is. So we have 18x + 9y = 7 The procedure is the same, so I trust you know the steps, we just need to be careful. So I subtract 18x from both sides to get:
9y = -18x + 7. Now I divide everything by 9 to get y by itself. This gives me
\[\frac{ 9y }{ 9 }=\frac{ -18x }{ 9 }+\frac{ 7 }{ 9 }\]This becomes:
\[y = -2x+\frac{ 7 }{ 9 }\]

So our slope for this line is -2. So if slopes are parallel, they have the same slope, which these of course don't. If they're perpendicular, then their signs are opposite and they are flipped upside down from each other. So given that we have positve 1/2,if we change its sign and flip it, we get -2. So these lines are perpendicular.

Answer 10

thank you