Equation of the line

[crackgmat007]

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

[sanjana]

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.

[crackgmat007]

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?

[sanjana]

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

[schumi_gmat]

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