Question

‎1.what is the value of K if the line 3x-2y=1 is perpendicular to the line y-(2K+1)x=3?
2.write an equation of the line in S.F.
a.having a slope of 2/3 and a y-intecept of -5
b.having a slope of -5 and passing through (2,-5)
c.with an x-intercept of -5 and a y-intercept of -3
d.parallel to y=2x-3 and passing through (3,-1)
e.perpendicular to y+1=3x and passing through (2,-3)
3. find y if the line through A(-1,2) and B(3,5) is parallel to the line through (0,-1) and (6,y)

Answer 1

when two lines are perpendicular to each other their slopes are related as
m1 = -1/m2
now you have two equations
3x-2y=1 and y-(2K+1)x=3
writing these equations in term of x we get
can you do it???

Answer 2

I can't
Please teach me !

Answer 3

ok

Answer 4

take the first equation

Answer 5

3x-2y=1
subtracting 3x from both sides we get
3x-3x-2y = 1-3x
-2y = 1-3x
now dividing both sides by -2 we get
y = 3/2x-1/2
got it???

Answer 6

Yes ! Then ? (:

Answer 7

now consider the second equation

Answer 8

y-(2K+1)x=3
adding (2K+1)x to both sides we get
y = (2K+1)x +3
clear???

Answer 9

then ?

Answer 10

now you have these both equations
y = 3/2x-1/2 and y = (2K+1)x +3
these both equations are in slope intercept form
as we know that the general form of slope intercept form is
y = mx+b
here m = slope and b = y-intercept

Answer 11

can you guess the slopes of these both lines now??

Answer 12

wait .
How about the K ?

Answer 13

we are getting to it but first find the slope

Answer 14

y = 3/2x-1/2
what is the slope now??

Answer 15

3/2

Answer 16

yes exactly

Answer 17

then ?

Answer 18

y = (2K+1)x +3
and the here the slope is ??

Answer 19

guess it we are one step away from finding K

Answer 20

2k+1 ?

Answer 21

hmm thats right

Answer 22

now these line are perpendicular to each other
thus their slopes are related as
m1 = -1/m2
here m1 = 3/2 and m2 = 2k+1

3/2 = -1/(2k+1)
can you solve for K now???

Answer 23

K=-1 ?

Answer 24

how you get that??

Answer 25

3/2=-1/2k+1
6k+3=-2
6k=-2-3
6k=-6
divided by 6
k=-1

Answer 26

no no its -5
-2-3 = -5

Answer 27

aw .
hah ! Sorry XD

Answer 28

so K = -5/6
is the required value of K

Answer 29

i think so ^^

Answer 30

it is the right answer verify it from the book

Answer 31

Yeah ! How about in number 2 ?

Answer 32

now you have
y-(2K+1)x=3
put in the value of K you got

Answer 33

do the last step and you are done

Answer 34

Done !
Correct ^^

Answer 35

are you sure??

Answer 36

how about letter d in number 2 ?

Answer 37

Yes !
100% sure ^_^

Answer 38

d.parallel to y=2x-3 and passing through (3,-1)
as two lines are parallel their slopes are equal
thus the slope from the given equation y=2x-3 is ???

Answer 39

find it

Answer 40

the slope is 2

Answer 41

ah ! I Get IT ^^

Answer 42

yes
so the equation of line you want to find will be having the same slope of 2
now you have slope and one point (3,-1)
use point slope form to get the equation

Answer 43

yes !
haha .. I get it ^^ New Achievement XD

Answer 44

but one mistake which i did is part a

Answer 45

In letter E ?

Answer 46

basically this was the question and by mistake i told you to put value of K in the equation y-(2K+1)x=3 so that was incorrect, so be sure you have done this part correctly

2.write an equation of the line in S.F.
a.having a slope of 2/3 and a y-intecept of -5

Answer 47

y=2/3x-5
isolate the 3 . Multiply both sides
3y=2x-15
-2x+3y=-15
multiply by -1
2x-3y=15

Answer 48

yes yes you are right

Answer 49

now go for part e

Answer 50

e.perpendicular to y+1=3x and passing through (2,-3) as i told you when two lines are perpendicular their slopes are related as m1 = -1/m2 so what is the slope from this equation y+1=3x

Answer 51

the slope is 3

Answer 52

yes now the slope of the line will will be perpendicular to it will be ???

Answer 53

Gets !

Answer 54

*which

Answer 55

as you have m1 = 3
m1 = -1/m2
now find m2

Answer 56

m2 is -1/3
the equation is x+3y=-4

Answer 57

use point slope form to get the equation

Answer 58

yap :)))

Answer 59

Yes ! Thank you so much ^^

Answer 60

i m sure your answer is correct

Answer 61

you are welcome and forgive my mistakes

Answer 62

Thanks !!! Haha ...

Answer 63

you are welcome

Answer 64

:))

Answer 65

Oh ! In number 3 :)

Answer 66

find y if the line through A(-1,2) and B(3,5) is parallel to the line through (0,-1) and (6,y)

Answer 67

then ?

Answer 68

first consider these points can you find the slope from these points??
A(-1,2) and B(3,5)

Answer 69

\[slope = \frac{ y2-y1 }{ x2-x1 }\]

Answer 70

then ?

Answer 71

so what is the slope???

Answer 72

3/4

Answer 73

yes
now consider the next two points
(0,-1) and (6,y)
can you find the slope??

Answer 74

same slope because it's parallel :))

Answer 75

yes but here what is the slope you got??

Answer 76

3/4

Answer 77

no no from the nest two points containing y

Answer 78

*next

Answer 79

the value of y is 7/2 ^^

Answer 80

(0,-1) and (6,y)
slope = (y+1)/6
now equate these slopes
(y+1)/6 = 3/4
y+1 = 18/4
y = 18/4 - 1

Answer 81

I used the equation slope=y2-y1/x2-x1
3/4=y+1/6-0
3/4=y+1/6
cross multiply
4y+4=18
4y=18-4
divided by 4
y=14/4
Simplest Form
y=7/2

Answer 82

yes yes thats right

Answer 83

by the way it seems to be like you are my teacher

Answer 84

haha ^^

Answer 85

keep your good and fast and accurate mathematics up

Answer 86

Thanks ^^

Answer 87

Thanks for the Time ^______^

Answer 88

welcome

Answer 89

:))