The image of an inverse scale function is shown in the figure. Point a is the upper point on the image, ab ⊥ X axis, AC ⊥ Y axis, and the perpendicular feet are B and C respectively. If the area of the rectangular aboc is 8, then the analytical expression of the inverse scale function is______ .

The image of an inverse scale function is shown in the figure. Point a is the upper point on the image, ab ⊥ X axis, AC ⊥ Y axis, and the perpendicular feet are B and C respectively. If the area of the rectangular aboc is 8, then the analytical expression of the inverse scale function is______ .

From the meaning of the question: S = | K | = 8, then k = ± 8; and because the image of the inverse proportion function is located in the first and third quadrant, K < 0, then k = - 8, the analytic expression of the inverse proportion function is y = - 8x. So the answer is: y = - 8x