Geometry

[Nishant]

Please help me with the DS question it is driving me insane?

If line L has a negetive slope and passes through (-5, A), is the x intercept of line L positive?

(1) The slope of line L is -5.
(2) A>0

By the way answer to do question is E, but I am convinced (as per the workout below) that answer is C. Please tell me wheter I am right ot wrong? And if possible how to get the right answer quickly?

I am not a graphical guy, so I would like to do this through algebra.

Equation of line: Y-y=m(X-x)
Thus, = A-y= -m(-5-x)
So equation of line is A-y=5m+mx, where A could be any constant.
To find X intercept, plug in y=0 and X=x. So,
A-0= 5m+mx
A-5m=mx
(A-5m)/m =x

We can rephrase our orignal question as: Does the value of x in expression "(A-5m)/m =x" positive or negetive.

Now its obvious 1 and 2 are insufficient on its own. But when we combine them, the expression will always be negetive (because numerator will always be positive, while denominator of the expression will always be negetive) . We have a defenative No. Thus C is sufficient.

Despite this answer to this question is E. Can you help me please?

[RonPurewal]

here's the source of the problem:

Equation of line: Y-y=m(X-x)
Thus, = A-y= -m(-5-x)
So equation of line is A-y=5m+mx, where A could be any constant.

in the two boldface steps, you've managed to turn "m" into "-m", seemingly by sheer magic.
you should leave "m" as "m", giving you
A - y = m(-5 - x)
A - y = -5m - mx

for the intercept:
A - 0 = -5m - mx
A + 5m = -mx
(A + 5m) / (-m) = x

if we take both conditions together, (A + 5m) becomes (A - 25), because m = -5.
this means that we don't know the sign of (A + 5m); it's positive if A is greater than 25, and negative if A is less than 25.
therefore, insufficient, so answer = e.

make sense?

--

by the way, it's interesting that you plugged in the values for 'big X' and 'big Y'; usually, the computations are easier if you plug the values in where you've written 'little x' and 'little y' (although you'll get the right answer either way).