Question

Select the pair of equations whose graphs are perpendicular.

A.
2y = –3x + 5
2x + 3y = 4

B.
y = 2x – 7
x + 2y = 3

C.
5x – 8y = 9
12x – 5y = 7

D.
x + 6y = 8
y = 2x – 8

Answer 1

@jim_thompson5910 @BlueEyedCountryGirl

Answer 2

hint: two lines are perpendicular if their slopes multiply to -1

example:

y = 2x + 3
y = -1/2x + 7

are perpendicular because 2*(-1/2) = -1

Answer 3

@jim_thompson5910 okay so what's the answer? Not trying to be rude.. haha

Answer 4

sorry I can't just give out the answers, but I can help you get there

Answer 5

are you able to solve for y?

Answer 6

Yeah well can you work through it with me?

Answer 7

how would you solve 2y = –3x + 5 for y?

Answer 8

how would you move that 2 over?

Answer 9

that's the part I don't get...

Answer 10

I mean I don't get the whole thing but this is also a problem.

Answer 11

well 2y means 2 times y

to move it over, you have to undo multiplication...so you have to divide both sides by 2

Answer 12

\[\Large 2y = –3x + 5\]


\[\Large y = \frac{–3x + 5}{2}\]


\[\Large y = \frac{–3x}{2} + \frac{5}{2}\]


\[\Large y = -\frac{3}{2}x + \frac{5}{2}\]


What is the slope here?

Answer 13

I honestly have no idea... sorry. I have a major gap from 5th grade till now.

Answer 14

you're familiar with y = mx+b right? or no?

Answer 15

sorry... no *winces*

Answer 16

that's ok, y = mx+b is the general form of any line where m is the slope and b is the y-intercept

Answer 17

the slope determines how steep/shallow the line is

the y-intercept moves the line up and down

so these two uniquely determine a line

Answer 18

compare \(\Large y = -\frac{3}{2}x + \frac{5}{2}\) to y = mx+b

what is m in this case?

Answer 19

-3/2 ??

Answer 20

good

Answer 21

now let's solve 2x + 3y = 4 for y

Answer 22

Yayy! I'm honestly so proud right now. :)

Answer 23

That's good. I'm glad you are. Let's solve the second equation for y.


\[\Large 2x + 3y = 4\]


\[\Large 3y = 4 - 2x\]


\[\Large 3y = -2x + 4\]


\[\Large y = \frac{-2x + 4}{3}\]


\[\Large y = \frac{-2x}{3} + \frac{4}{3}\]


\[\Large y = -\frac{2}{3}x + \frac{4}{3}\]


What is the slope here?

Answer 24

I...don't know :/

Answer 25

what is m in this case?

Answer 26

go back to y = mx+b

Answer 27

okay give me a min.

Answer 28

ok

Answer 29

is it 2???

Answer 30

compare \(\Large y = -\frac{2}{3}x + \frac{4}{3}\) to y = mx+b

Answer 31

oh so -2/3 ?

Answer 32

yep, so the two slopes of the two equations are -3/2 and -2/3

Answer 33

what do they multiply to?

Answer 34

so multiply those?

Answer 35

-1? or 1?

Answer 36

you have two negative numbers multiplied

Answer 37

so is the result negative? or positive?

Answer 38

1. Positive 1.

Answer 39

good

Answer 40

since the result is NOT -1, that means the two lines are NOT perpendicular

Answer 41

Oh okay..

Answer 42

so...

Answer 43

I have ten mins to finish this test....