The abscissa of the intersection m of the image of a linear function and the line y = 2x + 1 is 2, and the ordinate of the intersection n of the image of a linear function and the line y = - x + 2 is 1:1 The abscissa of the intersection m of the image of a linear function and the line y = 2x + 1 is 2, and the ordinate of the intersection n of the image of a linear function and the line y = - x + 2 is 1 Find: (1) the analytic expression of this linear function (2) The area of the triangle formed by the image of this function and the coordinate axis

The abscissa of the intersection m of the image of a linear function and the line y = 2x + 1 is 2, and the ordinate of the intersection n of the image of a linear function and the line y = - x + 2 is 1:1 The abscissa of the intersection m of the image of a linear function and the line y = 2x + 1 is 2, and the ordinate of the intersection n of the image of a linear function and the line y = - x + 2 is 1 Find: (1) the analytic expression of this linear function (2) The area of the triangle formed by the image of this function and the coordinate axis

Let y = KX + B be the image equation of this first-order function
And the line y = 2x + 1, then (1-B) / (K-2) = 2
If it is combined with the line y = - x + 2, then (2k + b) / (K + 1) = 1
The solution is k = 4, B = - 3
y=4x-3
The intersection points with the coordinate axis are (0, - 3), (3 / 4,0) respectively
Then the area s = 3 / 2 * 3 / 4 = 9 / 8