Hi, Bunuel!

Is it necessary to find the equation of line in absolute values of 'a' and 'b'? I mean the point (a,b) is given. Can't we just take 'a' and 'b' as known values because point (a,b) is mentioned?
My first thought while solving this question was that slope is given and point (a,b) is given through which the line passes. Only 'c' is unknown to find the equation of line. Taking each of the statements one by one, i was able to find the value of 'c' in terms of 'a' or 'b' and hence the equation of line in terms of all the known values i.e 'a' and 'b' was obtained.
So, this way each statement was sufficient according to me and I thought D to be the answer.

Please, clarify my this doubt.Thank you.

Sorry to be dense about this - if the line passes through points (1,-1); (0,0) and (2,-2), then we know both the slope and the x intercept. So we know the equation of the line?

We want to find the equation of line k. The diagram there shows TWO possible lines for k: RED and GREEN. They have different equations. So, we cannot get one single equation to answer the question.
_________________

But the lines do not satisfy b = -a. For example, where the lines cross the x axis should be (0,0), but we can see these lines have x values of -2 and -1 respectively

Bunuel

Not sure what you are trying to say there.

We are told that k passes through the point (a, b). (1) says that a = -b. The image above shows two possible cases (out of infinitely many) for the point (a, b):
If a = 1 and b = -1, then the equation of k is -x/2 - 1/2.
If a = 2 and b = -2, then the equation of k is -x/2 - 1.
_________________

I don't agree with the approach in the solution.
I have first found out the equation for perpendicular line in terms of a and b. I did this to make sure this isn't a c-trap question where one of the DS options could have just negated a and b.
Perpendicular line's equation : 2y + x = 2b + a. Assume, if choice 1 gives you (1. a = -2b), then the answer would be A.
After finding the perpendicular line, it was clear to me either of the DS options can't give an equation, so we need both and I marked the answer as C.

Bunuel ..

Is the equation of Line perpendicular to y=2x (Passing through Point (a,b) is y-b = -1/2 (x-a) + c ??
If yes, we don't Know the value of C. If no, could you elaborate?

The equation of a straight line that passes through a point \(P_1(x_1, y_1)\) with a slope m is: \(y-y_1=m(x-x_1)\).

So, the equation of a straight line that passes through a point \((a, b)\) with a slope -1/2 is: \(y-b=-\frac{1}{2}(x-a)\).


For Coordinate Geometry check:

24. Coordinate Geometry

• Theory
  Math: Coordinate Geometry
  Beauty of Coordinate geometry
  Dealing with Tangents on the GMAT
  
  • Questions
    DS Questions
    PS Questions

For more check:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

Can we link similar questions?