Question

is 4y=5x+2 and 8x=3-10y perpendicular
@jim_thompson5910

Answer 1

Well how do you determine whether two lines are perpendicular or not?

Answer 2

what does that mean exactly

Answer 3

when 2 lines are perpendicular is when they form a 90º angle when they touch

Answer 4

so that means that they are right

Answer 5

you would have to see, because that is the condition for them to be perpendicular, you need to put both functions in y=mx+b form so you can determine whether they are or not. it depends solely in the slope of the lines you are analyzing

Answer 6

The slopes would be opposite reciprocals.

Answer 7

so first you have to transform your 4y=5x+2 to y=mx+b, that's quite easy, you just need to divide both sides by 4 (you may have learnt this as "passing" the 4 multiplying the y dividing to the other side)

Answer 8

so it's as simple as \[4y=5x+2,(4y)/4=\frac{ 5x+2 }{ 4 }, y=\frac{ 5 }{ 4 }x+\frac{ 2 }{ 4 }\]

Answer 9

in the formula y=mx+b, the slope is "m", in this case it would be 5/4

Answer 10

to determine whether or not 2 lines are perpendicular by using only their formulas, the slope of one should be the opposite by multiplication of the other and with the opposite sign. What this means is that if we have a line of any slope (lets call it "a") the condition that MUST be covered in order for any other line to be perpendicular is that its slope (lets call it b) must be: \[b=-a ^{-1}=-\frac{ 1 }{ a }\]

Answer 11

so lets get the other slope shall we

Answer 12

our first slope is 5/4, we have to get the second one from \[8x=3-10y, (8x)-3=(-10y+3)-3, 8x-3=-10y,y=-\frac{ 8x-3 }{ 10 }=-\frac{ 8 }{ 10 }x+\frac{ 3 }{ 10 }\]

Answer 13

\[y=-\frac{ 8 }{ 10 }x+\frac{ 3 }{ 10 }=-\frac{ 4 }{ 5 }x+\frac{ 3 }{ 10 }\]

Answer 14

so, now we have the 2 slopes, and we know that fot them to be perpendicular the condition \[b=-\frac{ 1 }{ a }\] should be complete, so our "a"= 5/4, and our b=-4/5\[-\frac{ 1 }{ a }=-\frac{ 1 }{ \frac{ 5 }{ 4 } }\]

Answer 15

that should be "b" right? can you tell me if it is?

Answer 16

no ??

Answer 17

are you sure?

Answer 18

do you know how to divide fractions?

Answer 19

yea but I have a lot of trouble with them

Answer 20

try it out, I know you can do it

Answer 21

okay I will try but what do I divdie

Answer 22

you have to divide \[-\frac{ 1/1 }{ 5/4 }\]

Answer 23

okay I got 0.05 am I ritte

Answer 24

-0.05

Answer 25

no, remember, when you are dividing fractions you do this \[\frac{ a }{ b }\div \frac{ c }{ d }=\frac{ ad }{ bc }\]

Answer 26

how would you do that if we have a=1 b=1 c=5 d=4?

Answer 27

1/1 divided by 5/4 = 15/14 ritte

Answer 28

no, ab is short for a*b, its a multiplication

Answer 29

it's easy, I know you can do it

Answer 30

1/20 because 1*1=1 and then 5*4=20

Answer 31

@SalvadorV

Answer 32

check again \[\frac{ a }{ b }\div \frac{ c }{ d }=\frac{ ad }{ bc }, \frac{ 1 }{ 1 }\div \frac{ 5 }{ 4 }=?\]

Answer 33

5/4

Answer 34

mmmm nope, check those letters again, see this

Answer 35

4/5

Answer 36

buut I still don't noe if they are perpendicular

Answer 37

ummmm hello @SalvadorV

Answer 38

remember which were the conditions I told you for them to be perpendicular?

Answer 39

so yes they are

Answer 40

sorry, I'm part timing explaining calculus to someone

Answer 41

remember it was that if b=-(1/a) then it was perpendicular

Answer 42

so b was -4/5

Answer 43

and a was 5/4

Answer 44

so if \[-\frac{ 1 }{ a }\] is the same as "b", then the lines are perpendicular

Answer 45

can you tell me if they are?

Answer 46

yess they are !! ritte

Answer 47

YES!!!!!!!! :D

Answer 48

yay thanks let me noe when yhu are done with calculus

Answer 49

I don't think I'll be done soon :/ it's a very wide subject and the person I'm helping doesn't quite understand it