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Coordinate geometry-GMAT PREP

by selango » Wed May 26, 2010 8:01 am
The y-intercept of a line l is 4. If the slope of l is negative,which of the following could be x intercept of l?

i) -1

ii) 0

iii) 6

A) i only

B) ii only

c) iii only

d)i and ii

e) 1 and iii

Can anyone this in detail?

OA C
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by gmatmachoman » Wed May 26, 2010 9:06 am
selango wrote:The y-intercept of a line l is 4. If the slope of l is negative,which of the following could be x intercept of l?

i) -1

ii) 0

iii) 6

A) i only

B) ii only

c) iii only

d)i and ii

e) 1 and iii

Can anyone this in detail?

OA C
I understand that when a line pass through the second or fourth quad the slope will be negative.

Since ,as per the stem Y is postive. So X has to be negative.

I picked x= -1

Am i missing any fundae? plz help me out!!
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by tpr-becky » Wed May 26, 2010 10:59 am
if the slope of a line is postive it goes uphill from left to right, negative goes downhill from left to right.

This line has a negative slope and intersects y at a postive number and then continues downhill as you go to the right - this means the line will intersect the x axis in the positive quadrant.
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by clock60 » Wed May 26, 2010 12:00 pm
y=kx+b,
here b=4
y=kx+4
kx=-4
k=-4/x

now let us pick answers
x=-1
k=-4/-1=4, but according to the query k-slope is -ve so x=-1 out

x=0.
k=-4/0-does not exist

x=6
k=-4/6=-2/3 -ve slope
so C wins
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by Patrick_GMATFix » Wed May 26, 2010 12:32 pm
A negative slope means a line that heads down and to the right. Because it crosses y at 4 (which means in the top half of the plane) headed down and to the right, the x-intercept (where the line crosses the x axis) must be on the right half of the plane. Every point on the right half of the plane has a positive x coordinate, so the x intercept must be positive. The answer is C

This is GMATPrep question 1429. You can practice similar questions if you have access to the Solutions Engine drill generator by selecting topic="Geometry, Coordinate" and difficulty="400-500"

Best of luck,
-Patrick
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by tanviet » Tue Jun 08, 2010 8:13 pm
I review slope and now can get right this question for 10 second

there are ONLY two kind of slope, negative and positive (easy to remember, right). and there are ONLY two kinds of Y=AX+B.

in the line which has negative slope, the upper-x-line part and arrow of x-line create an angle which is larger than 90

in the line which has positive slope, the upper--x-line part and arrow of x-line create an angle which is smaller 90

remember the UPPER- X- LINE PARTand ARROW, and two angle. to do slope questionS in 10 seconds.
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by Patrick_GMATFix » Tue Jun 08, 2010 8:52 pm
your point is valid and your advice is good. Just want to point out to others who may not know that not all lines have slopes that are negative or positive. There are also flat lines (example y = 5) and vertical lines (example x = 5)
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by neerajkumar1_1 » Wed Jun 09, 2010 5:22 am
becky has explained it well... but if u have a problem visualizing the figure u can try algebraically as follows:

Equation of a line is given by
y=mx+c

Given y intercept is 4
therefore: at x=0 y=4 or in other terms c=4
=> y=mx+4
=> mx=y-4

We need to find the range for x intercept,
Since the x intercept is a value for y=0

=> mx= - 4

Also Given that slope is negative

x= - 4/m Where m is -ve

Therefor x has to be positive....

Hope this solves ur query...
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