1. Definition and definition formula: The independent variable X and the dependent variable Y have the following relationship: y=kx+b(k, b is a constant, k≠0), then Y is a linear function of X, especially when b=0. II. Properties of linear function: the change value of Y is in direct proportion to the corresponding change value of X, and the ratio is k, namely Images and properties of linear functions: 1. Exercise and Graphics: Through the following three-step list (1); (2) tracking points; (3) Connecting lines can make images of linear functions-straight lines. So the image of a function only needs to know two points and connect them into a straight line. 2. Property: any point P(x, y) on the linear function satisfies the equation: y = kx+b.3. Quadrant where k, b and function images are located. When k > 0, the straight line must pass through the first and third quadrants, and y increases with the increase of x; When k 0, the straight line must pass through the first and second quadrants. When b < 0, the straight line must pass through three or four quadrants. Especially, when b=O, the straight line passing through the origin o (0 0,0) represents the image of the proportional function. At this time, when k > 0, the straight line only passes through one or three quadrants; When k < 0, the straight line only passes through two or four quadrants. Four. Determine the expression of linear function: known point A(x 1, y1); B(x2, y2), please determine the expressions of the linear functions that pass through points A and B. (1) Let the expression of the linear function (also called analytic expression) be y = kx+b. (2) Because any point on the linear function P(x, y) satisfies the equation y = kx+B. Therefore, two equations can be listed. (3) Solve this binary linear equation and get the values of k and b. (4) Finally, get the expression of linear function. V. The application of linear function in life 1. When the time t is constant, the distance s is a linear function of the speed v, and s=vt .2. When the pumping speed f of the pool is constant, the water quantity g in the pool is a linear function of the pumping time t ... Set the original water quantity in the pool. g=S-ft