xy plane

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baller12q: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sat Mar 28, 2009 11:28 am

by baller12q » Tue Mar 31, 2009 3:24 pm

in the xy plane line k has a positive slope and and x-intercept 4. if the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k

a. -6
b. -4
c. -3
d. 3
e. 6

please explain how you get the right anwser

Source: Beat The GMAT — Problem Solving | Tue Mar 31, 2009 3:24 pm

El Cucu: Master | Next Rank: 500 Posts; Posts: 236; Joined: Fri Nov 28, 2008 9:16 am; Thanked: 9 times

Re: xy plane

by El Cucu » Tue Mar 31, 2009 5:29 pm

baller12q wrote:in the xy plane line k has a positive slope and and x-intercept 4. if the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k

a. -6
b. -4
c. -3
d. 3
e. 6

please explain how you get the right anwser

IMO E
Positive slope cut x in 4 (the line is descending from up left to down right) So the base of the triangle is 4.
Then 4*Y/2=12
Answer y=6
Is a 3-4-5 triangle

cm47323: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Tue Oct 21, 2008 12:10 pm; Thanked: 3 times; GMAT Score:770

by cm47323 » Tue Mar 31, 2009 7:00 pm

Area = 1/2(bh) = 12
.5(4)h=12
h=6

so the absolute value of the y-intercept is 6. We can't know it is positive or negative unless we know more about line k. Since we know it has a positive x-intercept and is positively sloped, its y-intercept is negative.

A

EricKryk: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Tue Mar 31, 2009 11:03 am; Thanked: 3 times

by EricKryk » Tue Mar 31, 2009 10:26 pm

cm47323 wrote:Area = 1/2(bh) = 12
.5(4)h=12
h=6

so the absolute value of the y-intercept is 6. We can't know it is positive or negative unless we know more about line k. Since we know it has a positive x-intercept and is positively sloped, its y-intercept is negative.

A

I agree fully. Thanks for the nice explanation

marcusking: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Feb 04, 2009 6:09 am; Location: Louisville, KY; Thanked: 8 times

by marcusking » Wed Apr 01, 2009 5:19 am

cm47323 wrote:Area = 1/2(bh) = 12
.5(4)h=12
h=6

so the absolute value of the y-intercept is 6. We can't know it is positive or negative unless we know more about line k. Since we know it has a positive x-intercept and is positively sloped, its y-intercept is negative.

A

I also arrived @ the answer the same way. Well done.

bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Sun Apr 04, 2010 8:38 am

hey could someone explain the reasoning behind the highlighted part ?

cm47323 wrote:Area = 1/2(bh) = 12
.5(4)h=12
h=6

so the absolute value of the y-intercept is 6. We can't know it is positive or negative unless we know more about line k. Since we know it has a positive x-intercept and is positively sloped, its y-intercept is negative.

A

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sun Apr 04, 2010 9:43 am

positive slope means the line is always be falling toward x axis
now base is 4;and area is 12 ;therefore ht is 6
since line is having a +ve x intercept and a +slope the line is in 4th quardant
hence ht is -6
A

bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Sun Apr 04, 2010 11:26 am

i get that.
But doesnt a positive slope rise from the 3rd quadrant towards the first quadrant ?

and a negative slope falls in the direction of second quadrant to the fourth quadrant???

If its rising from the 3rd quadrant(being a +ve slope), the positive x intercept would be in the first quadrant....and so would the y intercept be. isnt it ?

Can someone please draw the direction of the slopes ?

thephoenix wrote:positive slope means the line is always be falling toward x axis
now base is 4;and area is 12 ;therefore ht is 6
since line is having a +ve x intercept and a +slope the line is in 4th quardant
hence ht is -6
A

pops: Master | Next Rank: 500 Posts; Posts: 148; Joined: Tue Jun 09, 2009 11:06 pm; Thanked: 7 times

by pops » Sun Apr 04, 2010 11:06 pm

baller12q wrote:in the xy plane line k has a positive slope and and x-intercept 4. if the area of the triangle formed by line k and the two axes is 12, what is the y intercept of line k

a. -6
b. -4
c. -3
d. 3
e. 6

please explain how you get the right anwser

Many members have posted answer as 6.
If the two points are (4,0) and (0,6)
then the slope of the line would be= (y1-y2)/(x1-x2)=(6-0)/(0-4)=6/-4 < 0
but slope is mentioned positive hence, -6 is correct

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