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The line k has a positive slope m and it passes through the point (-4,

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The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 18 Feb 2015, 02:29
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The line k has a positive slope m and it passes through the point (-4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m?

A. 1/4
B. 3/4
C. 5/4
D. 7/4
E. cannot be determined
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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 18 Feb 2015, 07:02
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(Figure attached)
Equation of line will be given by
y-6 / (x- (-4)) = m
or, y = mx + 4m + 6

Area of triangle formed by line k and x and y-axis = area of Triangle AOB = (1/2) AO * OB = (1/2)*(4m+6)*(4m+6)/m = 54 (given)

Simplifying we will get
16m^2 + 48m + 36 = 108m
=> 16m^2 - 60m + 36 = 0
=> 4m^2 - 15m + 9 = 0
=> 4m^2 - 12m - 3m + 9 =0
=> 4m ( m-3) -3 (m-3) = 0
=> m = 3 , 3/4

So, answer will be B
Hope it helps!

Prjwl99 wrote:
The line k has a positive slope m and it passes through the point( -4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m?
a)1/4
b)3/4
c)5/4
d)7/4
e)cannot be determined

the ans is B

Could anyone please explain the method for reaching the answer
thanks in advance

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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 18 Feb 2015, 08:28
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I am not sure if my way of approach is correct. But still I ended up with the answer..

Area of the triangle formed by the line k with X & Y axis is 54.
1/2 * Base * Height = 54

Here Base refers to the x-intercept in units and Height refers to the y-intercept in units
So --> X (or Base) * Y (or Height) = 108

We know that the line k passes through the point (-4,6) and has a positive slope.
Therefore, the point where the line meets the X-axis must be definitely greater than -4 i.e greater than 4 units from the origin(Base)
Similarly, the point where the line meets the Y-axis must be definitely greater than 6 i.e greater than 6 units from the origin(height)

There are a handful of factors that multiply into 108 but only one satisfies the above condition.
9 and 12 -- valid since it satisfies both of the above criteria

the below ones do not
27 and 4
18 and 6
36 and 3
108 and 1

So the y intercept can be either (0,12) or (0,9)
and x-intercept can be either (-9,0) or (-12,0)

We slope m = (y2-y1)/(x2-x1) --> 12/9 or 9/12 i.e 4/3 or 3/4

Answer is 3/4 (B)
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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 18 Feb 2015, 08:39
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AVRonaldo wrote:
I am not sure if my way of approach is correct. But still I ended up with the answer..

Area of the triangle formed by the line k with X & Y axis is 54.
1/2 * Base * Height = 54

Here Base refers to the x-intercept in units and Height refers to the y-intercept in units
So --> X (or Base) * Y (or Height) = 108

We know that the line k passes through the point (-4,6) and has a positive slope.
Therefore, the point where the line meets the X-axis must be definitely greater than -4 i.e greater than 4 units from the origin(Base)
Similarly, the point where the line meets the Y-axis must be definitely greater than 6 i.e greater than 6 units from the origin(height)

There are a handful of factors that multiply into 108 but only one satisfies the above condition.
9 and 12 -- valid since it satisfies both of the above criteria

the below ones do not
27 and 4
18 and 6
36 and 3
108 and 1

So the y intercept can be either (0,12) or (0,9)
and x-intercept can be either (-9,0) or (-12,0)

We slope m = (y2-y1)/(x2-x1) --> 12/9 or 9/12 i.e 4/3 or 3/4

Answer is 3/4 (B)


Your reasoning is ABSOLUTELY SOUND.

Now what surprises me is how can someone which such reasoning skills end up with a score of 39 in Quant.
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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 28 Feb 2015, 10:10
Prjwl99 wrote:
The line k has a positive slope m and it passes through the point( -4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m?
a)1/4
b)3/4
c)5/4
d)7/4
e)cannot be determined

the ans is B

Could anyone please explain the method for reaching the answer
thanks in advance



check out the attached solution . let me know if case of questions.
thanks
Lucky
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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 29 Apr 2016, 14:13
Hi Bunuel

Please recognize the approach here. Is it right to try the different factors that produce 108 or you have more reliable and shorter way.
Actually, I solved in such way but it took me 4 Mins to complete the operation.
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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 05 Sep 2017, 10:59
someone please help me to understand how did you find 108?? please post your replies with formula and additional steps to make it clear for freshers.
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The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post Updated on: 06 Sep 2017, 13:12
The line k has a positive slope m and it passes through the point (-4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m?

A. 1/4
B. 3/4
C. 5/4
D. 7/4
E. cannot be determined

assume the line rising from the x axis to (-4,6) is the height of a 6-8-10 right triangle
thus, the triangle base on the x axis will run 8 units from (-4,0) to (-12,0)
we now know two points on line k: (-4,6) and (-12,0)
m=[6-0/-4-(-12)]=6/8=3/4
B

Originally posted by gracie on 05 Sep 2017, 16:49.
Last edited by gracie on 06 Sep 2017, 13:12, edited 1 time in total.
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The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 05 Sep 2017, 20:15
1
SandhyAvinash wrote:
someone please help me to understand how did you find 108?? please post your replies with formula and additional steps to make it clear for freshers.


The triangle area is (x*y)/2=54 => x*y=108

Now rise/run=slope
=> (y-6)/(x+4)=m
=> y=xm+4m+6

=> (4m+6)*(4m+6)/m=108
Solve this we find m = 3 or 3/4

Thus answer is B
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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 06 Sep 2017, 10:51
kelindoan wrote:
SandhyAvinash wrote:
someone please help me to understand how did you find 108?? please post your replies with formula and additional steps to make it clear for freshers.


The triangle area is (x*y)/2=54 => x*y=108

Now rise/run=slope
=> (y-6)/(x+4)=m
=> y=xm+4m+6

=> (4m+6)*(4m+6)/m=108
Solve this we find m = 3 or 3/4

Thus answer is B


hi kelindoan step 3 is still unclear how did you find this statement to solve for m??? please help
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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 21 Sep 2017, 00:17
1
SandhyAvinash wrote:
kelindoan wrote:
SandhyAvinash wrote:
someone please help me to understand how did you find 108?? please post your replies with formula and additional steps to make it clear for freshers.


The triangle area is (x*y)/2=54 => x*y=108

Now rise/run=slope
=> (y-6)/(x+4)=m
=> y=xm+4m+6

=> (4m+6)*(4m+6)/m=108
Solve this we find m = 3 or 3/4

Thus answer is B


hi kelindoan step 3 is still unclear how did you find this statement to solve for m??? please help


Hi,

Hope you understood till equation y=xm+4m+6
Now we need values of x and y intercepts here (nothing but value of x and y)
x intercept => 0= xm+4m+6 (place y=0)
from her we get x = -(4m+6) / m
similarly for y intercept , place x = 0 .... so y =4m+6

But the distances x and y are absolute values.. so we can remove negative sign

Hope you understood now..

Please let know in case of any doubts..

If it helps, kudos please :)
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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 27 May 2018, 22:11
BrushMyQuant wrote:
(Figure attached)
Equation of line will be given by
y-6 / (x- (-4)) = m
or, y = mx + 4m + 6

Area of triangle formed by line k and x and y-axis = area of Triangle AOB = (1/2) AO * OB = (1/2)*(4m+6)*(4m+6)/m = 54 (given)

Simplifying we will get
16m^2 + 48m + 36 = 108m
=> 16m^2 - 60m + 36 = 0
=> 4m^2 - 15m + 9 = 0
=> 4m^2 - 12m - 3m + 9 =0
=> 4m ( m-3) -3 (m-3) = 0
=> m = 3 , 3/4

So, answer will be B
Hope it helps!

Prjwl99 wrote:
The line k has a positive slope m and it passes through the point( -4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m?
a)1/4
b)3/4
c)5/4
d)7/4
e)cannot be determined

the ans is B

Could anyone please explain the method for reaching the answer
thanks in advance



Hi Bunuel, BrushMyQuant,
Using the 2 points at the X and Y axes and the point through which the line passes, following are the equations for slope that I came up with:

\(\frac{(y-6)}{(0+4)} = \frac{(6-0)}{(-4-x)}\)

from this, the equation I get is \(6x-4y+xy = 0\)
=> \(4y=6x -108\)

that gives us a slope of 3/2 which isnt an answe choice. Could you please help understand where am I going wrong?
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Re: The line k has a positive slope m and it passes through the point (-4, [#permalink]

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New post 27 May 2018, 22:37
Top Contributor
Hi Shruti0805,

Couple of things:

1. You are assuming that if a line is passing through point (-4,6) then it will pass through (0,6) and (-4,0) which is not true. See attached figure for reference.
2. The equation of a line passing through two points is (y-y1)/(x-x1) = y2-y1)/(x2-x1) so it will be (y-6)/(x-0) = (0-6)/(-4-0) and not (y-6)/(0+4) = (6-0)/(-4-x)
3. Equation of a line will always be a one degree equation in terms of x and y like ax + by+ c = 0, where a,b,c are constants.

hope it helps!
Shruti0805 wrote:
BrushMyQuant wrote:
(Figure attached)
Equation of line will be given by
y-6 / (x- (-4)) = m
or, y = mx + 4m + 6

Area of triangle formed by line k and x and y-axis = area of Triangle AOB = (1/2) AO * OB = (1/2)*(4m+6)*(4m+6)/m = 54 (given)

Simplifying we will get
16m^2 + 48m + 36 = 108m
=> 16m^2 - 60m + 36 = 0
=> 4m^2 - 15m + 9 = 0
=> 4m^2 - 12m - 3m + 9 =0
=> 4m ( m-3) -3 (m-3) = 0
=> m = 3 , 3/4

So, answer will be B
Hope it helps!

Prjwl99 wrote:
The line k has a positive slope m and it passes through the point( -4,6). the area of the triangle formed by k, the x axis and y axis is 54 square units. What is the possible value for m?
a)1/4
b)3/4
c)5/4
d)7/4
e)cannot be determined

the ans is B

Could anyone please explain the method for reaching the answer
thanks in advance



Hi Bunuel, BrushMyQuant,
Using the 2 points at the X and Y axes and the point through which the line passes, following are the equations for slope that I came up with:

\(\frac{(y-6)}{(0+4)} = \frac{(6-0)}{(-4-x)}\)

from this, the equation I get is \(6x-4y+xy = 0\)
=> \(4y=6x -108\)

that gives us a slope of 3/2 which isnt an answe choice. Could you please help understand where am I going wrong?

Attachments

Image.jpg
Image.jpg [ 41.91 KiB | Viewed 291 times ]


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Re: The line k has a positive slope m and it passes through the point (-4,   [#permalink] 27 May 2018, 22:37
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