Question

find the equation of the straight line which makes equal intercepts on the axes and passes through points (2,-7)

Answer 1

@hartnn please help

Answer 2

sure

Answer 3

:)

Answer 4

the equation of line can be y=mx+c
do u know how to get the intercepts?

Answer 5

yeah! If we need to find y intercept then we'll take x=0

Answer 6

so find x and y intercepts for me.

Answer 7

for that I'll have to find m first
How would I do that?

Answer 8

put x=0 in y=mx+c
u get
y=c<-----y-intercept.
put y=0 in y=mx+c
0=mx+c
mx=-c
x= -c/m <----x-intercept

Answer 9

and?

Answer 10

but did u get that?
now the line makes equal intercepts, so you have
x intercept= y-intercept
c= -c/m
can u find m from here ?

Answer 11

yep m= -1

Answer 12

absolutely! (if you want you can remember that slope of line with equal intercepts is always -1, or you can do this exercise)
so now your equation is y=-x+c
ok?

Answer 13

yeah

Answer 14

u have point (x,y)=(2,-7) on it
so just substitute x=2 and y=-7 in y=-x+c
and find c, try it

Answer 15

I did that but what would be the equation?

Answer 16

what is c ?

Answer 17

-5

Answer 18

-7=-2+c
c= -5, correct.
u had slope m=-1, u got c= -5
just put it in
y=mx+c

Answer 19

ohk and here too m= -1 right?

Answer 20

its the same line! yes, slope = m= -1

Answer 21

x + y + 5 =0

Answer 22

that is correct!
did u understand everything?

Answer 23

yeah thanks a lot! You are an amazing tutor ;)

Answer 24

welcome ^_^

Answer 25

thanks for the compliment :)

Answer 26

:)

Answer 27

Refer to the attachment.

Answer 28

how did u get that graph @robtobey ,the equation and intercepts are incorrect there.

Answer 29

how is m=1 ?

Answer 30

in your graph, u have y-intercept=-9 and x-intercept=9
so the intercepts are only equal in magnitude,
if the question intends to have intercepts of equal magnitude, the there will be two lines as solution, one yours y=x-9, and one what we have derived, x+y+5=0.
since the question asks for only one line, we assume that both intercepts must be equal in magnitude and sign, which gives the equation as x+y+5=0 only.

Answer 31

Well the attachment below should do the trick, from the Mathematica program.