To solve the moving point problem, we must first understand the meaning of the problem, understand the whole process of motion and the change of the graph, then draw the graph according to the classification discussion of the motion process, and finally find the equivalent relationship equation for different situations to solve.

For the moving point problem based on the number axis, there are often two different solutions because of the characteristics of the number axis itself.

One is to find the equivalent relationship according to the analysis of the relationship between "shape", that is, to solve it by using the number relationship equation between each line segment.

The other is to find the equivalent relationship from the aspect of "number", that is, to form equations by using the internal relationship between numbers represented by points on the number axis.

brief introduction

The thinking method of combining numbers and shapes is one of the main lines of mathematics teaching content. The following problems can be solved by using the idea of combining numbers with shapes:

1. set problem: In the set operation, the intersection, union and complement operations of sets are often handled with the help of the number axis and venn diagram, thus simplifying the problem and making the operation quick and clear.

2. Function problem: It is a common method to study the properties of functions with the help of images. The geometric features and quantitative features of function images are closely combined, which embodies the characteristics and methods of combining numbers and shapes.

3. Equation and inequality: When dealing with the equation problem, the problem of the root of the equation is regarded as the intersection of two function images; When dealing with inequality, we should start from the conditions and conclusions of the topic, contact the related functions, focus on analyzing its geometric significance, and find out the solution ideas from the graphics.