Two related quantities, one of which changes and the other changes with it. If the ratio (that is, quotient) of the two numbers corresponding to these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. Represented by letters: If the letters X and Y are used to represent two related quantities and K is used to represent their ratio, the (certain) proportional relationship can be expressed as: X. X and Y represent two related quantities, and K represents their ratio. Two related quantities change at the same time, in the same direction and with the same multiple. If the constant value in the ratio is called k, and the front and back terms are x and y respectively, then k=x/yk is the ratio of two numbers. The change law of two related quantities is in direct proportion: expansion at the same time, contraction at the same time, and the ratio remains unchanged. X/Y = K(。

Properties of positive proportional function

The proportional function y=kx(x is an arbitrary real number) has the following properties:

(1) When k > 0, the image of the proportional function passes through the first and third quadrants; When the value of the independent variable x increases gradually, the value of y also increases gradually.

(2) When k < 0, the image of the proportional function passes through the second and fourth quadrants; When the value of independent variable x increases gradually, the value of y decreases gradually. For the direct proportional function of practical problems, its image is sometimes only a part of a straight line (line segment, ray or just some points), which depends on the definition domain.