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Images and properties of linear functions in junior high school mathematics
Function is a very important knowledge point in junior high school mathematics. The following summarizes the relevant knowledge points of linear function in junior high school mathematics for your reference.

Images and properties of linear function 1 Any point P(x, y) on a linear function satisfies the equation: y = kx+b.

2. The coordinate of the intersection of the linear function and the Y axis is always (0, b), and the coordinate of the intersection of the linear function and the X axis is always (-b/k, 0).

3. The image of the proportional function always passes through the origin.

4. The relationship between k, b and the quadrant where the function image is located:

When k>0, y increases with the increase of x; When k < 0, y decreases with the increase of x.

When k>0, b>0, the straight line passes through the first, second and third quadrants;

When k>0, b<0, the straight line passes through the first, third and fourth quadrants;

When k < 0, b>0, a straight line passes through the first, second and fourth quadrants;

When k < 0, b<0, a straight line passes through the second, third and fourth quadrants;

When b=0, 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 the first and third quadrants; When k < 0, the straight line only passes through the second and fourth quadrants.

Definition of linear function In general, a function in the form of y = kx+b (k, b is a constant, k≠0) is called a linear function, where x is an independent variable. When b=0, the linear function y=kx, also known as the proportional function.

The analytical form of 1. linear function is y = kx+b, and judging whether a function is a linear function is to judge whether it can be transformed into the above form.

2. When b=0 and k≠0, y=kx is still a linear function.

3. When k=0 and b≠0, it is not a linear function.

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