The general shape is ykxb(k, b is constant, 0k? ) is called a linear function, where x is the independent variable. What time? When, the linear function ykx? , also known as proportional function.

(1) The analytical form of linear function is ykxb. Judging whether a function is a linear function is to judge whether it can be transformed into the above form.

(2)0b? ，0k？ When, ykx? It is still a linear function.

(3) When is 0b? ，0k？ It is not a linear function.

(4) Proportional function is a special case of linear function, which includes proportional function.

2. Positive proportional function and its properties

Generally speaking, a function in the form of y=kx(k is a constant and k≠0) is called a proportional function, where k is called a proportional coefficient. Note: The general form of the proportional function is y=kx (k is not zero) 1k is not zero, and the exponent of x is 1 3b is zero.

When k>0, the straight line y=kx rises from left to right through three or one quadrant, that is, y also increases with the increase of x; When k < 0,? The straight line y=kx passes through the second and fourth quadrants and decreases from left to right, that is, y decreases with the increase of x.

(1) Analytical formula: y=kx(k is a constant, k≠0) (2) Necessary point: (0,0), (1, k)

(3) Trend: k>0, the image passes through the first and third quadrants; K< at 0 o'clock? The image passes through two or four quadrants (4): k >; 0, y increases with the increase of x; K<0, Y decreases with the increase of the inclination angle of x (5): the larger the |k|, the closer it is to the Y axis; The smaller the |k|, the closer it is to the X axis.

3. Linear function and its properties

Generally speaking, if the shape is y=kx+b (k, b is constant, k≠0), then y is called a linear function of X. When b=0, y=kx+b means y=kx, so the proportional function is a special linear function.

Note: the general form of linear function is y=kx+b (k is not zero) 1k is not zero; ② The exponent of x is13b; Take any real number.

The image with linear function y=kx+b is a straight line passing through two points (0, b) and (-kb, 0). We call it straight line y=kx+b, which can be regarded as the translation of straight line y=kx to unit length of |b|. (When b>0, translate upward; When b<0, translate downward)