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xy-plane,

by grandh01 » Tue Sep 25, 2012 8:56 pm
In the xy-plane, the slope of line k is 3/2 . Does line k pass
through the point (-1,-4)?
(1) Line k passes through the point (1,-1)
(2) Line k passes through the point (3, 2)

oa is D
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Source: — Data Sufficiency |

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by Anurag@Gurome » Wed Sep 26, 2012 4:16 am
We can get the equation of line with slope and a point on the line.
So as slope is given in the question, and in the options we have a point on the line. we will get the equation of the lines in both cases.
m = 3/2, y = mx +c, we need to substitute the point co-ordinates to get the c.
once we know the equation, for finding whether the point passes through the line, we need to verify whether the co-ordinates of the point satisfy the equation.

using option 1,
(x,y) = (1,-1)
-1 = 1.5*1 + c
c = -2.5
so equation of the line -> 3/2*x - y -2.5 = 0
substitute (-1,-4) in the equation
3/2*(-1) - (-4) - 2.5 = 0
so, the point (-1,-4) passes through the line.
hence, can be answered by A alone.

using option 2,
2 = 3/2 * 3 + c
c = -2.5
so equation of the line -> 3/2*x - y -2.5 = 0
substitute (3,2) in the equation
3/2*(3) - (2) - 2.5 = 0
so, the point (3,2) passes through the line.
hence, can be answered by B alone.

hence, it is D
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