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When the area of the triangle formed by the line L passing through the point P (2,3 / 2) and the positive half axis of two coordinate axes reaches the minimum, the equation of line L is obtained
y=k(x-2)+3/2
Intersection with coordinate axis at (0,3 / 2-2k) and (2-3 / 2K, 0)
Area = 0.5 * (3 / 2-2k) * (2-3 / 2K) = 0.5 [6 - (4K + 9 / 4K)]
(4k+9/4k) ≥√4k*9/4k=3
Area ≤ 0.5 [6-3] = 1.5 if and only if 4K = 9 / 4K, i.e. 16K & # 178; = 9K = ± 3 / 4
When k = 3 / 4
The intersection points are (0,0) (0,0), so it is not advisable
When k = - 3 / 4
The intersection points are (0,3) (4,0) respectively, which can meet the conditions
So the linear equation is y = - 3 / 4 (X-2) + 3 / 2 = 3-3x / 4
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