the perpendicular line will have a slope of -1/2 (m1 m2 = -1 ... for perpendicular lines)
now to form the equation, all we need is any other point on this perpendicular line..

statement1) a = -b
can have many values of a and b ... so we will get diff eqns...
insufficient...

statement 2) again can have many values of a and b ... so we will get diff eqns...
insufficient...

together,
we can get the value of (a,b) a point on the perpendicular line...
we have the slope...
so we can form the equation
Pick C


ps: i feel as though i am missing something more, by which i could have solved by one of the statements all by itself...
anyways... for now i will stick with C...

goyalsau 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

The slope of line perpendicular to y = 2 x is -½, let its equation be y = - ½ x + c, where c is its y-intercept, which is to be determined, in other words. Since, y = - ½ x + c passes through (a, b), therefore c = b + ½ a.

[1] a + b = 0 doesn't solve b + ½ a uniquely; insufficient

[2] a - b = 1 doesn't solve b + ½ a uniquely; insufficient


When taken together, both a and b, hence b + ½ a, and hence c [spoiler]can be determined uniquely.


C[/spoiler]