"Using linear equations of two variables to determine linear function expressions" PPT courseware for linear equations of two variables

Description

"Using linear equations of two variables to determine linear function expressions" PPT courseware for linear equations of two variables

teaching objectives

1. Understand the respective characteristics of methods for constructing function graphs and algebraic methods.

2. Master the expression of a linear function using a system of linear equations of two variables.

3. Further understand the connection between equations and functions, and realize the universal connection between knowledge and the mutual transformation between knowledge.

Linear functions and linear equations of two variables can be transformed into each other, and they are unified from form to content.

The solution to a system of linear equations of two variables corresponds to the coordinates of the intersection of the graphs of linear functions corresponding to these two equations. ----Image method to solve linear equations of two variables

(1) Write a function (2) Make a graph (3) Find the intersection (4) Write the solution

Induction: Generally, each system of linear equations of two variables corresponds to two __________, so it also corresponds to two ______. From a "number" perspective, solving a system of equations is equivalent to considering the values ​​of the two functions when the independent variables are equal, and what the value of this function is; from a "form" perspective, solving a system of equations is equivalent to determining two The coordinates of the straight line ______.

2. Make use of systems of equations to solve function problems

The relationship between linear equations of two variables and linear functions is quite close. Flexible application of their intimate cooperative relationship of "number" and "shape" will help us solve problems.

What is the connection between a system of linear equations in two variables and a linear function?

The solution of a system of linear equations of two variables is the intersection coordinate of their corresponding graphs of two linear functions; conversely, the intersection point of the graphs of two linear functions is also the solution of their corresponding system of linear equations of two variables.

Places A and B are 100 kilometers apart. Two people, A and B, ride bicycles toward each other from places A and B respectively. Assuming that they all keep driving at a constant speed, the distance s (kilometers) from each of them to point A is a linear function of the riding time t (hours). After 1 hour, person B will be 80 kilometers away from point A; after 2 hours, person A will be 30 kilometers away from point A. Question: How long did it take for the two to meet?

1 hour later, B is 80 kilometers away from point A, that is, B's speed is 20 kilometers/hour

At 2 o'clock, A is 30 kilometers away from A, so A's speed is 15 kilometers/hour

Do you understand what he is thinking? Do it his way!

The problem can be solved using linear equations of one variable.

How to determine the relationship:

1) Set up a relationship;

2) Find the corresponding values ​​of X and Y;

3) Substitute into equation (group)

4) Solve equations (sets);

5) Write the relationship expression.

Like this, the method of first setting up the functional relational expression, and then determining the coefficients of the unknown numbers in the expression according to the given conditions, to obtain the functional expression is called the undetermined coefficient method.

1. In order to encourage residents to save water, a city's water company adopts a segmented charging method based on monthly water consumption. If a household's water fee y (yuan) is payable, the functional relationship between the water consumption x (t) and the water consumption x (t) is as shown in the figure.

(1) Write the functional relationship between y and x when 0≤x≤15 and x>15 respectively;

(2) If a user consumes 10 tons of water in October, how much water fee should he pay? If the user paid a water bill of 51 yuan in November, how many tons of water did he use in that month?

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For more information about the PPT courseware "Determining the expression of a linear function using a system of linear equations in two variables using a system of linear equations in two variables", please click on the PPT tag "Determining the expression of a linear function using a system of linear equations in two variables" PPT tag.

"Determining linear function expressions using linear equations of two variables" PPT teaching courseware for linear equations of two variables:

"Using a system of linear equations of two variables to determine the expression of a linear function" PPT teaching courseware for a system of linear equations of two variables Part 1: Knowledge points Basic knowledge point 1 The relationship between a system of linear equations of two variables and a linear function 1. Known straight line y=3x- The coordinates of the intersection of 3 and y=-3/2x+b..

"Using a system of linear equations of two variables to determine the expression of a linear function" PPT download of the system of linear equations of two variables:

"Determining linear function expressions using linear equations of two variables" PPT download of linear equations of two variables, 32 pages in total. Part One: Learning Objectives Use the method of undetermined coefficients to find linear function expressions and use linear equations of two variables to find linear function expressions for practical problems... ...

"Using a system of linear equations of two variables to determine the expression of a linear function" System of linear equations of two variables PPT:

"Using a system of linear equations of two variables to determine the expression of a linear function" System of linear equations of two variables PPT, 22 pages in total. Part One: Learning Objectives 1. Be able to use a system of linear equations of two variables to determine the expression of a linear function. (Key point) ... ... ... using a system of linear equations of two variables..

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Update Time: 2024-09-05

This template belongs to Mathematics courseware Beijing Normal University Edition Eighth Grade Mathematics Volume 1 industry PPT template

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