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

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

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26 Mar 2015, 03:45
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25% (medium)

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77% (01:49) correct 23% (02:07) wrong based on 229 sessions

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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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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 [ 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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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)

Attachments

121.gif [ 5.09 KiB | Viewed 4216 times ]

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Posts: 53020
Re: In the xy-coordinate system, line k has y-intercept 12 and an x-interc  [#permalink]

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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 [ 23.62 KiB | Viewed 4124 times ]

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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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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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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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02 Feb 2019, 07:05
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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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