"Application of linear functions" PPT courseware

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"Application of linear functions" PPT courseware

Related knowledge links

1. How to draw the graph of a linear function.

Usually, a straight line drawn through two points (-b/k, 0) and (0, b) is the image of the function y=kx+b (k≠0).

2. Undetermined coefficient method.

First set up the unknown numbers in the expression, and then use equations or systems of equations to determine these unknown numbers based on the given conditions. This method is called the undetermined method.

3. The image and properties of a linear function.

Image: The image of a linear function y=kx+b (k≠0) is a straight line, usually called the straight line y=kx+b.

Properties: For a linear function y=kx+b, when k>0, y increases with the increase of x; when k<0, y decreases with the increase of x.

Observe and think

We know that the measurement units of temperature in various countries around the world are not uniform. The commonly used units are Celsius (˚C) and Fahrenheit (˚F). The conversion relationship between them is as shown in the following table:

(1) Observe the table above. If the Celsius temperature and Fahrenheit temperature in the table are both regarded as variables, is the functional relationship between them a linear function? How did you discover it?

The Fahrenheit temperature y is regarded as a function of x. A rectangular coordinate system is established. The value of each pair (x, y) in the table is used as the coordinate of the point. Draw the corresponding points in the table in the rectangular coordinate system and observe whether these points are in the same position. On a straight line.

(2) Can you use the image in (1) to write the functional expression of y and x?

(3) In addition to the method mentioned by Xiaoliang, can you analyze the quantitative relationship between the two variables in the above table and judge that there is a linear functional relationship between them?

(4) Can you find out what the Celsius temperature is when the Fahrenheit temperature is 0 degrees (ie 0˚F)?

When y=0, 0=1.8x+32, the solution is x=-160/9, so when the Fahrenheit temperature is 0˚F, the Celsius temperature is -160/9˚C.

Warm up

In order to welcome the arrival of the new school year, Times Middle School plans to purchase a total of 20 basketballs and volleyballs before the start of school. It is known that basketballs are 80 yuan each and volleyballs are 60 yuan each. Assume that x basketballs are purchased, and the total cost of purchasing basketballs and volleyballs is y yuan. .

(1) Find the functional expression of y and x;

(2) If the number of basketballs is required to be no less than three times the number of volleyballs, how should it be purchased to minimize the total cost? What is the minimum fee?

Example 1 Shanqing Forest Farm plans to purchase a total of 800 saplings of two types, A and B. The saplings of type A are 24 yuan each, and the saplings of the same species are 30 yuan each. According to relevant information, the survival rates of saplings A and B are 85% respectively. , 90%.

(1) If the total cost of purchasing these two kinds of saplings is 21,000 yuan, how many saplings of A and B were purchased?

(2) In order to ensure that the total survival rate of this batch of saplings is not less than 88%, how many saplings of type A can be purchased at most?

(3) Under the conditions of (2), how to purchase saplings to minimize the cost of purchasing saplings? And ask for the lowest fee.

Try your hand

There are 20 workers in a workshop. It is known that each worker can produce 6 parts of type A or 5 parts of type B every day, and can earn a profit of 150 yuan for each type A part manufactured, and 260 yuan for each type B part manufactured. Yuan, the workshop arranges x workers to make parts of type A every day, and the remaining workers make parts of type B.

(1) Please write down the functional relationship between the daily profit y (yuan) and x (name) of this workshop;

(2) If you want the daily profit of the workshop to be no less than 24,000 yuan, how many workers do you think should be sent to manufacture Type B parts?

Extension after class

1. As shown in the figure below, L1 reflects the relationship between the sales revenue and sales volume of a company's products, and L2 reflects the relationship between the sales cost and sales volume of the company's products.

Question 1: How is this image different from the image seen in the previous lesson?

Question 2: Can you tell what the independent variables and dependent variables of the functions represented by these two functions refer to?

Question 3: Can you tell what quantities the x-axis and y-axis represent?

2. As shown in the figure below, L1 reflects the relationship between the sales revenue and sales volume of a company's products, and L2 reflects the relationship between the sales cost and sales volume of the company's products.

Answer based on the image:

1) When the sales is 2 tons,

Sales revenue is _______ yuan.

The cost of sales is _______ yuan.

2) When the sales is 6 tons,

Sales revenue is _______ yuan.

The cost of sales is _______ yuan.

The company made a profit of _______ yuan.

Keywords: Teaching courseware for the application of linear functions, Qingdao edition eighth grade mathematics volume 2 PPT courseware download, eighth grade mathematics slide courseware download, application of linear functions PPT courseware download, .PPT format;

For more information about the "Application of a Single Function" PPT courseware, please click on the "Application of a Single Function ppt" tab.

Download the PPT courseware of "Application of a linear function":

"Application of linear functions" PPT courseware download Part 1: Warm-up exercises 1. A car is driving from Nanjing to Shanghai, which is 300 kilometers away. When its average speed is 100 kilometers/hour, which graph below represents the distance s (kilometers) and the driving time t of the car from Shanghai..

"Application of a Single Function" PPT download:

"Application of a linear function" PPT download Part 1: Teaching objectives: 1. Experience the process of applying a linear function to solve practical problems. 2. Improve the ability to obtain information from text, tables, and images. 3. Understand the relationship between functions and equations through practical problems.

"Application of a linear function" PPT:

"Application of linear functions" PPT Part 1 content: The new lesson introduces A riding a bicycle and driving along the road at a speed of 10 kilometers. Three hours after departure, B riding a motorcycle started from the same place and drove in the same direction as A along the highway at a speed of 25 kilometers per hour. Suppose A leaves and exits...

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Update Time: 2024-07-29

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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