Equation of the line

Given Line :

Y=2X
We need to find the eqn of the line that passes through (a,b) and is perpendicular to Y=2X,
So if we can find (a,b) and the slope we can plug it into y=mx+b and get the equation of the line.

Statement 1:

a=-b
From this we cant find a or b, so not sufficient

Statement 2

a-b=1,again we cant find a or b,so insufficient

Combining 1 and 2

-2b=1
b=-1/2

Therefore a = 1/2

Now (a,b) = (1/2,-1/2)

The line passes through (a,b) and is perpendicular to y=2x
Slope of y=2x is 2
Therefore slope of the line perpendicualr will be -1/2

Therefore we have (a,b) and we have the slope so we can find the eqn of the line.
Hence C.

Thanks for the explanation. Looking back at the question, since equation of one line is given as y=2x, with slope 2, am I right to say that we can find the slope of perpendicular line, which must be negative reciprocal ie -1/2?

Yes,absolutey!

2 things to remember here,

For two lines with slopes M1 and M2,

(1)If they are parallel : M1=M2
(2)If they ae perpendicular : MIM2=-1

crackgmat007 wrote:What is the equation of the line that is perpendicular to line y=2x and passes through point (a,b)?

1. a = - b
2. a - b = 1

OA C

The eq of perpendicular line passing through (a,b): b=-a/2 + c (c = y intercept)

from (i) a = -b
c = b/2
Therefore, we dont know the eq of the line

from (ii) a - b=1
b+a/2 = c

Inusfficient

Hence we need (i) and (ii) to solve the equation

ANS C