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

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Intern
Joined: 10 Feb 2015
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The line k has a positive slope m and it passes through the point (-4, [#permalink]

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18 Feb 2015, 02:29
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Difficulty:

95% (hard)

Question Stats:

58% (02:55) correct 42% (03:27) wrong based on 166 sessions

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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
Director
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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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18 Feb 2015, 07:02
3
2
(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

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

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##### General Discussion
Manager
Joined: 24 Jan 2015
Posts: 71
GMAT 1: 590 Q39 V31
GPA: 4
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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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18 Feb 2015, 08:28
3
1
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

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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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18 Feb 2015, 08:39
1
1
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

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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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

check out the attached solution . let me know if case of questions.
thanks
Lucky
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Manager
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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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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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05 Sep 2017, 10:59
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The line k has a positive slope m and it passes through the point (-4, [#permalink]

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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.
Intern
Joined: 31 Aug 2017
Posts: 7
The line k has a positive slope m and it passes through the point (-4, [#permalink]

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05 Sep 2017, 20:15
1
SandhyAvinash wrote:

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

Manager
Joined: 05 Oct 2016
Posts: 93
Location: United States (OH)
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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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06 Sep 2017, 10:51
kelindoan wrote:
SandhyAvinash wrote:

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

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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21 Sep 2017, 00:17
1
SandhyAvinash wrote:
kelindoan wrote:
SandhyAvinash wrote:

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

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..

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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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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

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

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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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

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

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 [ 41.91 KiB | Viewed 291 times ]

_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

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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