1. Definition of linear equation: linear equation is a mathematical expression describing a straight line. On the two-dimensional plane, the general form of linear equation is ax+by+c=0, where a and b are slope and intercept, and c is intercept. The slope of a straight line is a numerical value describing the inclination of the straight line relative to the X axis, and the intercept is the coordinate value of the point where the straight line intersects the Y axis on the Y axis.
2. Distance formula between two points: Given the coordinates of two points (x 1, y 1) and (x2, y2), the distance between two points can be calculated by the following formula: d=√[(x2-x 1)? +(y2-y 1)？ This formula will be used to solve linear equations, because the distance between two points on a straight line is a fixed value after being determined.
3. Slope of the straight line: For two points (x 1, y 1) and (x2, y2) on the straight line, the slope of the straight line can be obtained by the following formula: k =(y2-y 1)/ (x2-x 1) The slope of the straight line is expressed as When k is a positive number, the straight line inclines to the upper right; When k is negative, the straight line inclines to the lower right.
4. Interception equation: According to the intercept and slope of a straight line, the intercept equation of a straight line can be derived: y=kx+b, where k is the slope of the straight line and b is the intercept. Substituting two known points into the equation, you can get the value of b, and you can get the linear equation.
The Application of Mathematics in Life
1. linear programming: linear programming is a mathematical method used to find the maximum or minimum value of a linear objective function given a set of constraints. Linear programming is widely used in real life, such as production planning and resource allocation. For example, in production planning, linear programming can be used to determine the best product mix to maximize profits.
2. Function model: Function model is to express the relationship between two or more variables with mathematical formulas. Function model has a wide range of applications in real life, such as prediction and analysis, optimization problems and so on. For example, in economics, functional models can be used to describe the relationship between supply and demand, predict the trend of price changes, and provide policy suggestions for the government and enterprises.