Question

Geometry help, please!!!

Determine if the lines are parallel, perpendicular, or neither.
#1)
y=1/2x+7
y-8=-2(x+9)

Answer 1

@Hero

Answer 2

1. Put the second equation in the form \(y = mx + b\)
2. Test the slopes using \(m_1m_2 = -1\) If their products = -1 then the lines are perpendicular.

Answer 3

y=1/2x+7
and
y-8=-2(x+9)
where do i go from here?

Answer 4

I just told you above what to do. Follow the steps.

Answer 5

I'm unsure of what to plug in

Answer 6

Like Hero said, isolate y
\(y-8=-2(x+9)\)
First we want to distribute to make this easier, can you do that?

Answer 7

y-8=-2(x+9)
y-8=-2x+18
y=-2x+10
is this right?

Answer 8

How come you didn't do that when I asked?

Answer 9

i didn't know what you meant when you said m-m1

Answer 10

$m_1$ and $m_2$ are the slopes from each line.

Answer 11

Not quite, you have to do \(-2 \times x \) + \(-2\times 9\)
\(-2 \times x \) is -2x and \(-2\times 9\) is -18 (You missed the sign transfer)
Then you have to add 8 on both sides, right idea
\(y-8=-2x-18\)

==> \(y=-2x-10\)

Keep the sign and you're good

Answer 12

All that matters really are the slopes.

Answer 13

You have them now multiply them together. If you get -1 then the lines are perpendicular.

Answer 14

Well true but I just want to show the whole process, shortening it might be confusing

Answer 15

I was unsure of the steps, thanks though Hero.

Answer 16

y=-2x-10 times y=1/2x+7
is
y=-2x+-70
????

Answer 17

Hero said to multiply the slopes

Answer 18

y=-1x+-70 ***

Answer 19

oh

Answer 20

so it is perpendicular, it =-1

Answer 21

Yep

Answer 22

https://www.desmos.com/calculator/mg3bxn27zh
Graphically (Not sure if you were allowed to use graphing calculators)

Answer 23

yeah, can't use graphing calcs

Answer 24

i have another, can i work it out and you check it?

Answer 25

Sure

Answer 26

y+3=5(x-4)
y-2=5(x+2)



y-2=5(x+2)
y+3=5x-20
y=5x+23
--
y-2=5(x+2)
y-2=5x+10
y=5x-8
--
5*5=25
?

Answer 27

I'm confused on your work, what did you do

Answer 28

If I'm reading this right
\(y+3=5x-20\\
y=5x+23\)

Watch your sign -20-3 ≠ [+]23