In the xy-plane, line m is a line that does not pass through the origi

Question

If line  m  does not pass through the origin, is the slope of line  m  negative ?

(1) The product of the x-intercept and the y-intercept of line  m  is positive.
 
(2) Line  m  passes through the points  (a, \ b)  and  (c, \ d) , where  \frac{b - d}{a-c} < 0  .

reto · Answer

Statement 1: 
Draw a coordinate plane with various lines intercepting so that the product of x-intercept and y-intercept is positive. In this case, m is always negative. Statement 1 > Sufficient.

Statement 2: 
Not quite sure. It seems insufficient because you do not know wheter (a-c) or (b-d) is negative or a fraction - which would be essential in order to calculate m.

VladimirKarpov · Answer

As I understand, the second statement gives us information about the slope (negative or positive). It does not matter (a - c)(b - d)<0 or (b-d)/(a-c)<0 => the slope is negative. So the answer is D

peachfuzz · Answer

Is the slope of line m is negative?

(1) The product the x-intercept and the y-intercept of line m is positive.
Drawing this on a coordinate plane, the allowable points will align so that the slope is always negative
sufficient

(2) I tested a few points, given this constraint (a - c)(b - d)<0
This statement seems sufficient as well as the slope is negative.

Answer: D

mehrdadtaheri92 · Answer

Answer should be D ...

Data 1) says that the line passes through points (a, b) in which their multiple is positive . it means that the sign of a and b are the same ( both are positive or both negative)

So, lest consider both scenarios : 1 ) if both a and b are negative in this case the line passes through areas 2, 3 , and 4 and we know that if a line passes through areas 2 and 4 its slope is

Negative. scenario 2 : if both a and b are positive then line passes through areas 1 , 2 and 4 and in this case the slope of the line is negative too. so both scenarios give us the same result

so this data is sufficient

Data 2 ) It says that line passes through points (a, b) and (c,d) in which (a-c)*(b-d) is Negative.

It means that either a<c and b>d OR a>c and b<d , so if we consider both scenarios and draw the line with different coordinates ( I can not draw Here :lol:

) we will see that

in both scenarios line passes through at least the areas 2 and 4 in the xy- plane . so this option is sufficient too

so , answer is D....

) we will see that in both scenarios line passes through at least the areas 2 and 4 in the xy- plane . so this option is sufficient too so , answer is D....

D3N0 · Answer

Ans: D
Solution: m does not pass through origin. IS slope -ve?
1) Product of x intercept and y intercept is positive. means either both -ve or both +ve.
 so the intercept can be at (+x,0) & (0,+y) OR (-x,0) & (0,-y)
 we have the two pints slope of the line m = in any of the two cases slope is -ve.

2)m passes through points (a,b) and (c,d) and we know (a-c)(b-d)<0 means either (a-c) is -ve OR (b-d) is negative.
 from this we can say that slope is negative for sure.

Ans: D

akhilbajaj · Answer

Untitled.png Line m does not pass through origin. Lets draw the possibilities as line 1 and 2 with negative slope and line 3 and 4 with positive slope. Intercepts are indicated in the figure assuming x,y are positive numbers.. St1- The product of the x-intercept and the y-intercept of line m is positive. Check the product of intercepts for the four options from the figure. for line 1, xy>0 for line 2, (-x)*(-y)>0 for line 3, (-x)*(y)<0 for line 4, (x)*(-y)<0 Thus, if product of intercepts >0, slope <0. Sufficient St2- Line m passes through the points (a, b) and (c, d), where (a - c)(b - d)<0 slope = (b-d)/(a-c) If (a - c)(b - d)<0, => (a - c) and (b - d) have opposite signs => slope = (b-d)/(a-c) <0 Sufficient. Answer D Press kudos if the graphical representation helped you.

23a2012 · Answer

the answer is D
statment 1 the product of the x-intercept and the y-intercept of line m is positive this case will be true only if the slep is negative.
statment 2 we tray different cases we will get that (a - c)(b - d)<0 only if the slep is negative.
for example (4,0) (0,-5) (0,4) (-5,0) when we draw these points we will see the result will be negative only if the slep is negative

Crytiocanalyst · Answer

The key to solving the problem is getting all the signs right

(1) The product of the x-intercept and the y-intercept of line m is positive.
y=c; x=-c/m
=>-C^2/m>0
this only if m<0
Hence suff

(2) Line m passes through the points (a, b) and (c, d), where (a - c)(b - d)<0
Eqn of a line in 2 point form we can get
(b - d)/(a - c)
and if (a - c)(b - d)<0 either (b - d)<0 or(a - c) negative
Both time yielding a negative slope
Suff
Hence IMO D

Bunuel · Answer

Official Solution:

If line  m  does not pass through the origin, is the slope of line  m  negative ? 
 
(1) The product of the x-intercept and the y-intercept of line  m  is positive. 
 
Since the product of the intercepts is positive, either both intercepts are negative ((negative, 0) and (0, negative)) or both intercepts are positive ((positive, 0) and (0, positive)). In either case, the line is sloping downwards as we move from left to right, so the slope of line  m  is negative. Sufficient.
 
(2) Line  m  passes through the points  (a, \ b)  and  (c, \ d) , where  \frac{b - d}{a-c} < 0  . 
 
The slope of a line is defined as "rise over run" or the change in  y  divided by the change in  x  between any two points on the line. In this case, the two points given are  (a,b)  and  (c,d) , so the slope of line  m  is  \frac{b - d}{a-c} , which is given to be negative in this statement. Hence, the slope of line  m  is positive. Sufficient.

Answer: D

In the xy-plane, line m is a line that does not pass through the origi

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In the xy-plane, line m is a line that does not pass through the origi

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