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

Question

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.

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

Kudos for a correct  solution .

Lucky2783 · Answer

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}

GMATinsight · Answer

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  A

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: boundedtriangle_text.PNG

law258 · Answer

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 -->  /  = -12/5

A

narendran1990 · Answer

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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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

Prep Toolkit

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