okletsdothis wrote:This is probably an easy sum. but Since I am weak in this subject can someone please help me.

Q.
If line k in the xy-coordinate plane has slope -3/2, does line k pass through the point (12, -13)?

(1) The point (6, -2) lies on line k.

(2) The point (2, 4) lies on line k.

OA D

General equation of a line is y = mx + b
where x,y are the variables that stand for the co-ordinates at any point on the line
m is the slope of the line
and b = y-intercept i.e. y- co-ordinate of the point where the line crosses the y-axis.

Given that m= -3/2 and x =12 and y = -13
Equating the values in the equation of a line:
-13 = ((-3/2) * 12) + b
rephrasing the question is b = 5?

(1) x = 6 and y = -2 and m = (-3/2) [already known from the stem]
Equating the values in the equation of a line:
-2 = ((-3/2) * 6) + b
b = 7.
As b is not equal to 5 this is a Definite NO. i.e. line k definitely does not pass through point (12, -13). a Definite NO means SUFFICIENT.

(2)x = 2 and y = 4 and m = (-3/2) [already known from the stem]
Equating the values in the equation of a line:
4 = ((-3/2) * 2) + b
b = 7.
As b is not equal to 5 this is a Definite NO. i.e. line k definitely does not pass through point (12, -13). a Definite NO means SUFFICIENT.


So, CORRECT ANSWER is (D) - each statement alone is sufficient.