文 [1]着重探索函数y =ax + bx (ab≠ 0 ) (1)的应用价值 ,文 [2 ]运用判别式法验证了函数 y=(ax +c) + bx +d(ab≠ 0 )的图象是双曲线 ,本文运用转轴法来探究双曲线 (1)及其平移状态的几何特征 .引理 1　对于双曲线 (1) ,当b 0时 ,把直线 y=ax到y轴的角的平分线记为x′轴 ,则 The paper [1] focuses on the application value of the function y =ax + bx (ab≠ 0) (1). The paper [2] uses the discriminant method to verify the function y=(ax +c) + bx +d(ab≠ 0 The image of the image is hyperbolic. In this paper, the method of turning axis is used to explore the geometric characteristics of the hyperbola (1) and its translation state. Lemma 1 For the hyperbola (1), when b 0, the straight line y=ax to the y axis The bisector of the angle is denoted by the x′ axis.