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.