"Linear function and proportional function" linear function PPT courseware 2

Description

"Linear function and proportional function" linear function PPT courseware 2

Review and Thoughts

1.What is a function?

In a certain change process, there are two variables x and y. If an x ​​value is given, a y value is determined accordingly, then we call y a function of x, where x is the independent variable and y is the dependent variable.

2.What are the expressions of functions?

Functions can be expressed in three ways: images, tables, and algebraic expressions.

Do it

1. The natural length of a certain spring is 3 cm. Within the elastic limit, for every 1 kilogram increase in the mass x of the hung object, the spring length y increases by 0.5 cm.

(1) Calculate the length of the hanging object when its mass is 1 kg, 2 kg, 3 kg, 4 kg and 5 kg respectively, and fill in the following table:

(2) Can you write the relationship between x and y? y=3+0.5x

2. The original oil in the fuel tank of a certain car is 100 L, and the car consumes 9 L of oil every 50 kilometers traveled.

(1) Complete the following table:

(2) Can you write the relationship between x and y? y=100-0.18x

Discuss

The above two functional expressions: (1) y=3+0.5x (2) y=100-0.18x. Let’s discuss. Is there any relationship between these two functional expressions? Please communicate among the groups.

Linear function: If the relationship between two variables x and y can be expressed in the form of y=kx+b (b is a constant, k is not equal to 0), then y is said to be a linear function of x. (x is the independent variable, y is the dependent variable.)

When b=0, y is said to be a proportional function of x.

practice

Among the following statements, the one with a proportional function relationship is ().

A. The area of ​​the rectangular flower bed remains unchanged, and the relationship between length y and width x;

B. The perimeter of the square remains unchanged, and the relationship between the side length x and the area S;

C. One side of the triangle remains unchanged, and the relationship between the height h on this side and S;

D. The area of ​​the circle is S, the radius is r, and the relationship between S and r.

2. As shown in the figure, in △ABC, the bisectors of ∠B and ∠C intersect at point P. Assume ∠A=x, ∠BPC=y, when ∠A changes, find the functional relationship between y and x , and determine whether y is a linear function of x.

Solution: y =1/2x + 90.

y is a linear function of x.

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For more information about the PPT courseware of "Larvic Functions and Proportional Functions", please click on the "Linear Functions ppt" linear functions and proportional functions ppt tag.

"Linear Functions and Proportional Functions" PPT courseware for linear functions:

"Linear function and proportional function" linear function PPT courseware learning objectives 1. Understand the concepts of linear function and proportional function, and the relationship between them. 2. Be able to write simple linear function and proportional function expressions according to the given conditions . What is a function?..

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Update Time: 2024-12-03

This template belongs to Mathematics courseware Beijing Normal University eighth grade first volume mathematics industry PPT template

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