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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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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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18 Feb 2015, 07:02
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(Figure attached) Equation of line will be given by y6 / (x (4)) = m or, y = mx + 4m + 6 Area of triangle formed by line k and x and yaxis = 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 ( m3) 3 (m3) = 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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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 xintercept in units and Height refers to the yintercept 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 Xaxis must be definitely greater than 4 i.e greater than 4 units from the origin(Base) Similarly, the point where the line meets the Yaxis 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 xintercept can be either (9,0) or (12,0)
We slope m = (y2y1)/(x2x1) > 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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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 xintercept in units and Height refers to the yintercept 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 Xaxis must be definitely greater than 4 i.e greater than 4 units from the origin(Base) Similarly, the point where the line meets the Yaxis 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 xintercept can be either (9,0) or (12,0)
We slope m = (y2y1)/(x2x1) > 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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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 Consider +1 Kudos if you like this post.
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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
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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05 Sep 2017, 16:49
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 6810 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=[60/4(12)]=6/8=3/4 B
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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05 Sep 2017, 20:15
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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 => (y6)/(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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06 Sep 2017, 10:51
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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 => (y6)/(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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21 Sep 2017, 00:17
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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 => (y6)/(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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