As shown in the figure, P is any point on the image with inverse scale function y = K / X (k > 0). The perpendicular line passing through point P is the x-axis. The perpendicular foot is point m. It is known that s triangle POM = 2 (1) Find the value of K (2) if the image of the line y = x and the inverse scale function intersects at point a in the first quadrant, find the analytic expression of the function of the line passing through point a and point B (0, - 2)

As shown in the figure, P is any point on the image with inverse scale function y = K / X (k > 0). The perpendicular line passing through point P is the x-axis. The perpendicular foot is point m. It is known that s triangle POM = 2 (1) Find the value of K (2) if the image of the line y = x and the inverse scale function intersects at point a in the first quadrant, find the analytic expression of the function of the line passing through point a and point B (0, - 2)

K = 4 because the area of the triangle POM is one-half * the bottom * the height (the bottom is exactly X and the height is y, which is essentially one-half XY), so xy = 4, and K = XY so = 4
First of all, k = 4, the function formula is y = 4 / x, and we combine it with y = x to get x = 2, y = 2, so the coordinate of a is (2,2), because B is (0, - 2)
So the function passing through points a and B is y = 2x-2