Question

The equation of a straight line passing through the point(-2,3) and making intercepts of equal lengths on the axes is?
2x+y+1=0
x-y=5
x-y+5=0
none of these..

Answer 1

I tried..
\[\LARGE \frac{x}{a}+\frac{y}{a}=1\]
\[\LARGE x+y=a\]
\[\LARGE -2+3=a..>a=1\]
\[\LARGE x+y=1\]'
where did i go wrong

Answer 2

I got two solutions. One of which is trivial.

The distance between (0, 0) and the y-intercept is equal to the distance between (0, 0) and the x-intercept.

y - 3 = m(x + 2)

The y-intercept is

y - 3 = 2m
y = 2m + 3

The x-intercept is

0 - 3 = m(x + 2)
-3/m = x+ 2
x =-2 - 3/m

Set the y-intercept equal to the x-intercept and solve for the slope, m.

One of these slopes will give you a line that passes through the origin itself. This one you can disregard as trivial.

Answer 3

for line having equal intercepts is of the form x+y=a since it passes through (-2,3)
we get for a
as -2+3=a
or a=1
thus the reqd line is x+y=1
so none of these..

Answer 4

@matricked that's what I did but the answer is C

Answer 5

y = 1 - x is the correct solution. Is that not equivalent to what you posted?

Answer 6

its incorrect! 101%

Answer 7

@DLS
then they might have mention that signs of inetrcept are opposite

Answer 8

no..!

Answer 9

if the intercepts are equal but of opposite sign then
the form will be x-y=a
and if u plug in (-2,3) u will get a=-5
hence line is x-y=-5
or x-y+5=0 ..... third option

Answer 10

Ah..that is a little different.

Answer 11

question is correct

Answer 12

I found a hint on solution on google..
see the pt. lies in 2nd quadrant....so the only way the line makes equal intercept is when it has slope +1.....using point-slope form of line...... (y-3)=+1(x+2)....... it will give ur required answer......

Answer 13

But clearly the equation y = 1 - x passes through (2, -3), and has intercept lengths of 1.

Answer 14

it is one of the lines passing through..it..there might be many lines

Answer 15

There are so many lines because only one condition is given. one of the line is x+y=1

Answer 16

but the option doesn't have that so we have to find another one...

Answer 17

If by "equal lengths" you mean have the same magnitude, then there are 3 such lines. One was given by @matricked, the other is y = 1 - x, and the third is the trivial case of y = -3x/2 where both intercepts are of 0 length.

Answer 18

@DLS
yup sometimes we have to think from all angles and find the closest answer

Answer 19

so how to get C?

Answer 20

the form will be x-y=a and if u plug in (-2,3) u will get a=-5 hence line is x-y=-5 or x-y+5=0 ..... third option

Answer 21

how x-y?

Answer 22

Use the equation I provided earlier, just switch the signs on one side of them. This gives a slope of 1, and thus y - 3 = x + 2 or y = x + 5 or x - y + 5 = 0

Answer 23

hold on ..

Answer 24

i didnt get m=1

Answer 25

\[\LARGE \frac{3}{m}-2=2m+3\]
\[\LARGE 2m^2-4m-2=0\]

Answer 26

Your first number should be -3/m

Answer 27

But this is the original equation that gives the line y = 1 - x. If you want to derive an equation where the two intercepts have equal length but opposite signs, you have to reverse the sign on one side of the equation.

Thus if our original equation is

-3/m - 2 = 2m + 3

Turn it into

3/m + 2 = 2m + 3

This will yield a slope of 1

Answer 28

well,,whenever in doubt, for competition questions , why dont you simply go for option checking,,yields correct ans also + saves times..
here,,only (3) matches..
and for the method
the eqns would be of the form

+-(x/a) +-(y/a) =1

Answer 29

+-(x/a) +-(y/a) =1?

Answer 30

4 permutations would be there,
+x , -y
+x , +y
-x , -y
-x , +y

Answer 31

the original eq isnt x/a+y/b=1?

Answer 32

it is, - and + will denote the quadrant it is in ..

Answer 33

cant we find slope=1
wouldn't the angle be tan45?
equal intercepts..

Answer 34

diagram kaisa hoga?

Answer 35

these are the 4 possibilities..

Answer 36

aur 1 possibility aur hai,,jab origin se pass hoga line..

Answer 37

\[\LARGE \frac{x}{-a}+\frac{y}{a}=1\]
ye hogi fir to?

Answer 38

ye bhi ho sakta hai..
check karna hoga bas..4 ans ho sakte hain..+5th,,origin wala..

Answer 39

how origin?

Answer 40

how do we get intercepts at origin?

Answer 41

jab intercepts 0 ho jayenge..

Answer 42

:o yes :/okay

Answer 43

thanks!

Answer 44

hmm.. kk :)

Answer 45

aur kaise pass kar sakti hai ?