Question

a line passes through the point (12, -1)
Sum of the intercept made by the axes is 7
what is the equation of the line?

Answer 1

can u find the intercepts ?

Answer 2

u can refer the question where you had equal intercepts....

Answer 3

how?

Answer 4

for the line y=mx+c
to get y-intercept, put x=0 in y=mx+c
to get x-intercept, put y=0 in y=mx+c

Answer 5

after that?

Answer 6

c + mc=7m ?

Answer 7

sum of intercepts = 7
so u get an equation with m and c.
use point (12,-1) to find other equation in m and c

Answer 8

y- intercept = c \(\checkmark\)
x- intercept = ??

Answer 9

I am not getting it :/

Answer 10

c/m

Answer 11

to get x-intercept, put y=0 in y=mx+c
0=mx+c
mx=-c
x= -c/m = x-intercept
sum = c-c/m = 7
or
mc - c = 7m

Answer 12

ohk and after that?

Answer 13

u have point 12,-1 on y=mx+c
12 = -m +c
or c= 12+m
substitute this c in
mc - c = 7m
you will get a quadratic in m
can u solve quadratic equations ?

Answer 14

go it :)

Answer 15

I again got stuck at the quadratic eqn
mc-m-19=0
after that?

Answer 16

c= 12+m

Answer 17

mc - c = 7m
c(m-1) = 7m
(m+12)(m-1) = 7m
m^2 +11m -12 =7m
m^2 + 4m -12= 0

Answer 18

solved it :)
Thanks a lot

Answer 19

got the values of m and c ?

Answer 20

m= 2 or -6

Answer 21

yup

Answer 22

which one to take?

Answer 23

so u have 2 lines here.....m=2,c=14
m=-6,c=6

Answer 24

both the lines satisfy given conditions, so both are correct

Answer 25

ohk so now?

Answer 26

ohk

Answer 27

y=mx+c
y=2x+14

y=-6x+6

Answer 28

oh, wait, 12,-1 does not satisfy y=2x+14
2(12)+14 is not -1

-6(12)+6 is still not -1.....
i am so sorry!!
i made a mistake while substituting the point!

Answer 29

u have point 12,-1 on y=mx+c
12 = -m +c <------NO

-1=12m+c
or c= -1-12m
substitute this c in
mc - c = 7m
you will get a quadratic in m
can u solve quadratic equations ?

Answer 30

i can

Answer 31

(-1-12m)(m-1)=7m
-12m^2+11m+1=7m
12m^2 - 4m -1=0

Answer 32

what will be the final equation then?

Answer 33

what values of m u got?

Answer 34

wait I am doing the whole thing again

Answer 35

sorry for that mistake.....

Answer 36

see I am getting the eqn 12m^2 -4m+1=0
is that right?

Answer 37

i worked it out to get 12m^2 - 4m -1=0
did u do any sign mistake?

Answer 38

I did...I corrected it now

Answer 39

so m= -1/2 or 1/6
now?

Answer 40

and c= -3 or 5

Answer 41

is that right?

Answer 42

check
m=1/2 or -1/6

Answer 43

check as in? How ? through which eqn?

Answer 44

12m^2 - 4m -1=0
m= 1/2 or -1/6
u got it as -1/2 ot 1/6 incorrectly....so i told u to verify again

Answer 45

see what I did is
12m^2 - 6m + 2m -1=0
is that okay?

Answer 46

yes

Answer 47

(6m+1)(2m-1)?

Answer 48

=0
yes

Answer 49

so its the same what I did before
How is it wrong?

Answer 50

(6m+1)(2m-1)=0
6m+1=0 or 2m-1=0
m=-1/6 or n=1/2

Answer 51

yeah now?

Answer 52

fin 2 corresponding values of c

Answer 53

after that?

Answer 54

did u get c as 1 or -7
?

Answer 55

m= -1/6, c= 1 ----> y=(-1/6)x+1
m= 1/2, c= -7----->y=x/2-7

Answer 56

I didn't get the value of c

Answer 57

c= -1-12m
= -1-12(-1/6) = ??

c= -1-12m
=-1-12(1/2) =??

Answer 58

I got it

Answer 59

:)