triangle and coordinates problem

[nailyad]

This is easy problem, still answered by me incorrectly:

In the XY plane line K has positive slope and X intercept 4. If the area of the triangle formed by line and two axes is 12 what is Y-intercept of the line K?

I answered this with -3 which was incorrect:

Aabc=A*4=12 therefore A is -3 ( positive slope)

Correct answer is -6. What am I missing here?
N

[manfromohio]

Area of a triangle is 1/2 * base * height - Base here is 4 units (X intercept)

So solving for height , absolute height = 6

Since a +ve slope line having a X-intercept at 4 can only have a -ve Y intercept (graph it to see), the answer is -6

[nailyad]

this is interesting, because I counted base as unknown and height is 4! How do we know how is the graph will look like????
Let me know your thoughts

Thank you
N

[linkinpark]

this is interesting, because I counted base as unknown and height is 4! How do we know how is the graph will look like????
Let me know your thoughts

Thank you
N

even if you assumed height to be 4 the formula for area of triangle = 1/2 * base * height will result other side as 6.
the reason is that x and y axes intersect each other perpendicularly at (0,0) so you can consider either side as base or height.