Point on line L?

[gibran]

Line L passes through point (1,4), and the product of its intercepts with axis-x and axis-y is negative. Which of the following point is on the line L?
A. (2,3)
B. (5,7)
C. (4,2)
D. (4,-1)
E. (5, -1)

OA:

SPOILER: B

Please help to explain with steps.

[krovvidy]

For the product of x & y intercepts to be negative, the line should have a positive slope
(since either x-int would be +ve & y-int would be -ve or vice-versa ... in both cases, the line segment between x & y intercepts would be in 2nd or 4th quadrants ... and hence the line would incline upwards when drawn left to right)

And only choice B has a positive slope ... 4-7 / 1-5

[GmatG]

Originally Posted by krovvidy

For the product of x & y intercepts to be negative, the line should have a positive slope
(since either x-int would be +ve & y-int would be -ve or vice-versa ... in both cases, the line segment between x & y intercepts would be in 2nd or 4th quadrants ... and hence the line would incline upwards when drawn left to right)

And only choice B has a positive slope ... 4-7 / 1-5

Can u explain this more.. For the product of x & y intercepts to be negative, the line should have a positive slope ?..

Thanks

[gmatcraze]

Originally Posted by krovvidy

For the product of x & y intercepts to be negative, the line should have a positive slope
(since either x-int would be +ve & y-int would be -ve or vice-versa ... in both cases, the line segment between x & y intercepts would be in 2nd or 4th quadrants ... and hence the line would incline upwards when drawn left to right)

And only choice B has a positive slope ... 4-7 / 1-5

Can someone please help to explain this concept in detail .... thanks

[Makumajon]

x-intercept*y-intercept=negative.

So, if the line cuts x-axis on positive side, then it must cut y-axis on negative side. Conversely, if the line cuts x-axis on negative side, then it must cut y-axis on positive side.

[Whatever the case, the angle between the line and positive side of x-axis will be less than 90 degree. You can easily see it by drawing a rough sketch. So, the slope of the line will be negative.]

Now we need two points to find the slope of a line:
Slope = difference in y-coordinates/difference in x-coordinates

We already have one point (1, 4). So, test the choices for the other probable point:
(A) point (2, 3). Slope = (3-4)/(2-1) = -1, negative
(B) point (5, 7). Slope = (7-4)/(5-1) = 3/4 = positive. Answer.

Shortcut: if x-coordinates are positively related with y-coordinates, slope is positive. Otherwise, negative.
Positively related means, when x increases, y will also increase. When x decreases, y will also decrease. So, when you get two points, look at the change of x's values and y's values.

[Test Taker]

Originally Posted by gmatcraze

Can someone please help to explain this concept in detail .... thanks

X intercept means the point where the line touches x-axis.Let it be 'a'.The point would be (a,0).

Y intercept means the point where the line touches y-axis.Let it be 'b'.The point would be (0,b).

Here the product of those intercepts is negative.

So a=+ve and b=-ve or
a=-ve and b=+ve

One point would be (+ve value,0),(0,-ve value).A line connecting these points would be in the 4th Quad.

In the second case,the point would be (-ve value,0) and (0,+ve value).A line connecting these points would be in the 2nd Quad.

When you move from left to right,the lines are going upward.So the slope is +ve.

[gmatcraze]

thanks a lot Makumajon and test_taker .... I've got it now!

[raunekk]

2good explanation kroviddy!!!

[Fiver]

Originally Posted by Makumajon

x-intercept*y-intercept=negative.

So, if the line cuts x-axis on positive side, then it must cut y-axis on negative side. Conversely, if the line cuts x-axis on negative side, then it must cut y-axis on positive side.

[Whatever the case, the angle between the line and positive side of x-axis will be less than 90 degree. You can easily see it by drawing a rough sketch. So, the slope of the line will be negative.]

Now we need two points to find the slope of a line:
Slope = difference in y-coordinates/difference in x-coordinates

We already have one point (1, 4). So, test the choices for the other probable point:
(A) point (2, 3). Slope = (3-4)/(2-1) = -1, negative
(B) point (5, 7). Slope = (7-4)/(5-1) = 3/4 = positive. Answer.

Shortcut: if x-coordinates are positively related with y-coordinates, slope is positive. Otherwise, negative.
Positively related means, when x increases, y will also increase. When x decreases, y will also decrease. So, when you get two points, look at the change of x's values and y's values.

Liked the shortcut given by you man. U rock.