Find an equation of the line passing through the point (1, 4) such that the area of the triangle formed by this line and the positive coordinate axes is as small as possible.

I know you I need to minimize the Area. And, I know I need to express the area in terms of one variable. But, when I try to write the equation of the line, I get messed up with the x-values. I think I'm labeling my diagram wrong. Any thoughts?

Question

Find an equation of the line passing through the point (1, 4) such that the area of the triangle formed by this line and the positive coordinate axes is as small as possible.

I know you I need to minimize the Area.  And, I know I need to express the area in terms of one variable.  But, when I try to write the equation of the line, I get messed up with the x-values.  I think I'm labeling my diagram wrong.  Any thoughts?

anonymous · Answer

I solved this but I don't think I did it in the most elegant way.  Anyone have an elegant solution?