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GMAT - Problem Solving - Coordinate geometry

In the xy-coordinate plane, which of the following points must lie on the line kx + 3y = 6 for every possible value of k?

In the xy-coordinate plane, which of the following points must lie on the line kx 3y = 6 for every possible value of k?

(A) (1,1)
(B) (0,2)
(C) (2,0)
(D) (3,6)
(E) (6,3)

The equation

kx + 3y = 6

can be written as the combination of two equations

kx = 0 -> x = 0

and 3y = 6 -> y = 2

(if we add both equations we get the equation of given line)

so the line must pass through (0, 2)

 

Alternatively

the equation kx + 3y = 6

will becoming independent of k only when x = 0, and since the point has to satisfy the equation for every value of k this has to be true.

so if x = 0

3y = 6 -> y = 2

thus the point will be (0, 2)

 

B. is correct