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In the xy-coordinate system, line k has y-intercept 12 and an x-interc

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In the xy-coordinate system, line k has y-intercept 12 and an x-interc  [#permalink]

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New post 26 Mar 2015, 03:45
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In the xy-coordinate system, line k has y-intercept 12 and an x-intercept greater than zero. If the area of the triangular region enclosed by line k and the two axes is 30, what is the slope of line k?

A. -12/5
B. -6/5
C. 6/5
D. 3/2
E. 12/5

Kudos for a correct solution.

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Re: In the xy-coordinate system, line k has y-intercept 12 and an x-interc  [#permalink]

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New post 26 Mar 2015, 05:36
Bunuel wrote:
In the xy-coordinate system, line k has y-intercept 12 and an x-intercept greater than zero. If the area of the triangular region enclosed by line k and the two axes is 30, what is the slope of line k?

A. -12/5
B. -6/5
C. 6/5
D. 3/2
E. 12/5

Kudos for a correct solution.



attached image to show that slope will be -ive , as X and Y intercept both are positive . for positive slope X and Y intercept should have opposite signs.
answer A . \(\frac{-12}{5}\)
Attachments

409791.jpg
409791.jpg [ 24.66 KiB | Viewed 4228 times ]

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In the xy-coordinate system, line k has y-intercept 12 and an x-interc  [#permalink]

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New post 26 Mar 2015, 06:02
1
Bunuel wrote:
In the xy-coordinate system, line k has y-intercept 12 and an x-intercept greater than zero. If the area of the triangular region enclosed by line k and the two axes is 30, what is the slope of line k?

A. -12/5
B. -6/5
C. 6/5
D. 3/2
E. 12/5

Kudos for a correct solution.


Y-intercept = 12
X-intercept= +ve
Draw figure with above inputs and you will find a line as shown in figure
i.e. Line has negative slope

Any Line that goes downward when drawn from Left to right represents NEGATIVE SLOPE.
Line with Negative Slope always passes throug Quadrants II and IV


Any Line that goes UPWARD when drawn from Left to right represents POSITIVE SLOPE.
Line with Positive Slope always passes through Quadrants I and III


Now only OPTION A and B remaining.

Slope of line = Y-intercept / X-intercept

Now area of Triangle = (1/2) Base x Height = (1/2) Base x 12 = 30
Base (X-intercept) = 5

i.e. Slope of Line = -(12/5)

Answer: Option
Attachments

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Re: In the xy-coordinate system, line k has y-intercept 12 and an x-interc  [#permalink]

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New post 30 Mar 2015, 02:35
Bunuel wrote:
In the xy-coordinate system, line k has y-intercept 12 and an x-intercept greater than zero. If the area of the triangular region enclosed by line k and the two axes is 30, what is the slope of line k?

A. -12/5
B. -6/5
C. 6/5
D. 3/2
E. 12/5

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
boundedtriangle_text.PNG
boundedtriangle_text.PNG [ 23.62 KiB | Viewed 4124 times ]

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In the xy-coordinate system, line k has y-intercept 12 and an x-interc  [#permalink]

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New post 31 Oct 2016, 16:02
Area of triangle = 1/2 (b)(h)

From the prompt, we know 30 = (1/2)(b)(12) --> Solve: b = 5

Coordinates of b = (5,0) & Coordinates of h = (12,0) --> Use slope formula --> [12-0]/[0-5] = -12/5

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In the xy-coordinate system, line k has y-intercept 12 and an x-interc  [#permalink]

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New post 10 Nov 2016, 04:58
Equation: y=mx+b, Y-intercept (b) is 12, solving for x-intercept, 0=mx+12, -12/m=x. Given that x>0, therefore 'm' has to be negative. Option A & B alone satisfy the condition.

Substituting m=-12/5, we get x=5. Therefore the two points are (5,0) & (12,0), plotting the points we can see that the area would be 30.
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Re: In the xy-coordinate system, line k has y-intercept 12 and an x-interc  [#permalink]

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Re: In the xy-coordinate system, line k has y-intercept 12 and an x-interc   [#permalink] 02 Feb 2019, 07:05
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