coordinate geometry

[sana.noor]

(70) Line D passes through point (-2,5), and the product of its x-intercept and yintercept is positive. Which of the following points could be on line D?

a) (5,10)
b) (-3,2)
c) (-1,7)
d) (-1,2)
e) (-3,1)

OA is D

[macattack]

Given the product of both intercepts is positive we know that these intercepts are of the same sign. On scratch paper draw a graph, place the point (-2,5) on the graph and think of possible lines that have intercepts of the same sign and passes through that point, you will directly notice that the slope should be negative in order to verify the given. Now that we did some mental geometry its time to apply what we got:
The slope is negative--->if x2>x1 then y2<y1 (This is high school Cartesian math if you have any inquiry please feel free to ask me). Now check the solutions.
x1=-2 y1=5
A:5>-2 and 10>5 (eliminate)
B:-2>-3 and 5>2 (eliminate)
C:-1>-2 and 7>5 (eliminate)
D:-1>-2 and 2<5 (yeyy!!)
E:-2>-3 and 5>1 (eliminate)

OA is D

Cheers

[GMATGuruNY]

(70) Line D passes through point (-2,5), and the product of its x-intercept and yintercept is positive. Which of the following points could be on line D?

a) (5,10)
b) (-3,2)
c) (-1,7)
d) (-1,2)
e) (-3,1)

OA is D

DRAW the figure:


For the product of its intercepts to be positive, Line D must look like one of the two options in the figure above.
Of the five answer choices, only (-1,2) could be on line D.

The correct answer is D.