Presentation "linear function and its graph". Linear function and its graph Linear function its properties and graph presentation

Stairs and railings 12.08.2021

Stairs and railings

slide 1

Algebra lesson in grade 7 "Linear function and its graph" Prepared by Tatchin U.V. mathematics teacher MBOU secondary school №3 city of Surgut

slide 2

Purpose: formation of the concept of "linear function", the skill of plotting its graph according to the algorithm Tasks: Educational: - to study the definition of a linear function, - to introduce and study the algorithm for plotting a graph of a linear function, - to work out the skill of recognizing a linear function according to a given formula, graph, verbal description. Developing: - to develop visual memory, mathematically literate speech, accuracy, accuracy in construction, the ability to analyze. Educational: - to cultivate a responsible attitude to educational work, accuracy, discipline, perseverance. - develop skills of self-control and mutual control

slide 3

Lesson Plan: I. Organizing time II. Actualization of basic knowledge III. Exploring a new topic IV. Consolidation: oral exercises, tasks for building graphs V. Solving entertaining tasks VI. Summing up the lesson, recording homework VII. Reflection

slide 4

I. Organizational moment Having guessed the words horizontally, you will learn the keyword 1. The exact set of instructions describing the procedure for the performer to achieve the result of solving the problem in a finite time 2. One of the coordinates of the point 3. Dependence of one variable on another, for which each value of the argument corresponds to a single value of the dependent variable 4. French mathematician who introduced the rectangular coordinate system 5. An angle whose degree measure is greater than 900 but less than 1800 6. The independent variable 7. The set of all points in the coordinate plane whose abscissas are equal to the values of the argument, and whose ordinates are equal to the corresponding values function values 8. The road we choose T G R A P H I K P R Y M A Z

slide 5

1. An exact set of instructions describing the procedure for the performer to achieve the result of solving the problem in a finite time 2. One of the coordinates of a point 3. Dependence of one variable on another, in which each value of the argument corresponds to a single value of the dependent variable 4. French mathematician who introduced a rectangular coordinate system 5. An angle whose degree measure is greater than 900 but less than 1800 6. Independent variable 7. The set of all points of the coordinate plane whose abscissas are equal to the values of the argument, and whose ordinates are equal to the corresponding values of the function 8. The road we choose A L G O R I T M A B S C I S S A F U N C T I A D E K H A R T T U P O J A R G U M E N T

slide 6

II. Actualization of basic knowledge Many real situations are described by mathematical models, which are linear functions. Let's take an example. The tourist traveled by bus 15 km from point A to point B, and then continued to move from point B in the same direction to point C, but on foot, at a speed of 4 km/h. At what distance from point A will the tourist be after 2 hours, after 4 hours, after 5 hours of walking? The mathematical model of the situation is the expression y = 15 + 4x, where x is the walking time in hours, y is the distance from A (in kilometers). Using this model, we answer the question of the problem: if x = 2, then y = 15 + 4 ∙ 2 = 23 if x = 4, then y = 15 + 4 ∙ 4= 31 if x = 6, then y = 15 + 4 ∙ 6 = 39 The mathematical model y = 15 + 4x is a linear function. A B C

Slide 7

III. Exploring a new topic. An equation of the form y=k x+ m , where k and m are numbers (coefficients) is called a linear function. To build a graph of a linear function, you need to specify a specific x value and calculate the corresponding y value. Usually these results are presented in the form of a table. They say that x is an independent variable (or argument), y is a dependent variable. 2 1 1 2 x x x y y x

Slide 8

Algorithm for plotting a graph of a linear function 1) Make a table for a linear function (associate each value of an independent variable with a value of a dependent variable) 2) Construct points on the xOy coordinate plane 3) Draw a straight line through them - a graph of a linear function Theorem The graph of a linear function y = k x + m is a straight line.

Slide 9

Consider the application of the algorithm to plot a linear function Example 1 Plot a linear function y = 2x + 3 1) Make a table 2) Plot points (0; 3) and (1; 5) in the xOy coordinate plane

slide 10

If the linear function y=k x+ m is considered not for all x values, but only for x values from some numerical set X, then we write: y=k x+ m, where x X (- membership sign) the variable can take on any non-negative value, but in practice a tourist cannot walk at a constant speed without sleeping and resting for as long as he likes. This means that it was necessary to make reasonable restrictions on x, say, a tourist walks for no more than 6 hours. Now let's write a more accurate mathematical model: y = 15 + 4x, x 0; 6

slide 11

Consider the following example Example 2 Plot a linear function a) y = -2x + 1, -3; 2; b) y = -2x + 1, (-3; 2) 1) Compile a table for the linear function y = -2x + 1 2) Construct points (-3; 7) and (2; -3) on the coordinate plane xOy and draw a straight line through them. This is a graph of the equation y = -2x + 1. Next, select the segment connecting the constructed points. x -3 2 y 7 -3

slide 12

slide 13

We are building a graph of the function y = -2x + 1, (-3; 2) How does this example differ from the previous one?

slide 14

slide 15

IV. Consolidation of the studied topic Choose which function is a linear function

slide 16

slide 17

slide 18

Complete the following task A linear function is given by the formula y = -3x - 5. Find its value at x = 23, x = -5, x = 0

slide 19

Verification of the solution If x = 23, then y = -3 23 - 5=-69 - 5 = -74 If x = -5, then y = -3 (-5) - 5= 15 - 5 = 10 If x = 0 , then y = -3 0– 5= 0 – 5= -5

slide 20

Find the value of the argument that makes the linear function y = -2x + 2.4 equal to 20.4? Verification of the solution At x = -9, the value of the function is 20.4 20.4 = - 2x + 2.4 2x =2.4 – 20.4 2x = -18 x= -18:2 x = -9

slide 21

The next task Without completing the construction, answer the question: the graph of which function does A (1; 0) belong to?

slide 22

slide 23

slide 24

slide 25

Name the coordinates of the points of intersection of the graph of this function with the coordinate axes With the OX axis: (-3; 0) Check yourself: With the OY axis: (0; 3)

Lesson objectives: to formulate the definition of a linear function, an idea of its graph; identify the role of parameters b and k in the location of the graph of a linear function; to form the ability to build a graph of a linear function; develop the ability to analyze, generalize, draw conclusions; develop logical thinking; skills building independent activity

Uk-badge uk-margin-small-right">

Answers 1. a; b 2. a) 1; 3 b) 2; x y 1. a; in 2. a) 2; 4 b) 1; x y option 2 option

Uk-badge uk-margin-small-right">

B k b>0b0 K 0b0 K"> 0b0 K"> 0b0 K" title="(!LANG:b k b>0b0 K"> title="b k b>0b0 K"> !}

B k b>0b0 y=kx I, III quarters Through the origin K 0b0 y=kx I, III quarters Through origin K"> 0b0 y=kx I, III quarters Through origin K"> 0b0 y=kx I, III quarters Through origin K" title="(!LANG:b k b> 0b0 y=kx I, III quarters Through the origin K"> title="b k b>0b0 y=kx I, III quarters Through the origin K"> !}

B k b> 0b0 y=kx I, III quarters Through the beginning of the K coordinate"> 0b0 y=kx I, III quarters Through the beginning of the K coordinate"> 0b0 y=kx I, III quarters Through the beginning of the K coordinate" title="(!LANG:b k b> 0b0 y=kx I, III quarters Through the beginning of the coordinates K"> title="b k b>0b0 y=kx I, III quarters Through the beginning of the coordinates K"> !}

B k b>0b0 y=kx I, III quarters Through the beginning of the coordinates K 0b0 y=kx I, III quarters Through the beginning of the K coordinate"> 0b0 y=kx I, III quarters Through the beginning of the K coordinate"> 0b0 y=kx I, III quarters Through the beginning of the K coordinate" title="(!LANG:b k b> 0b0 y=kx I, III quarters Through the beginning of the coordinates K"> title="b k b>0b0 y=kx I, III quarters Through the beginning of the coordinates K"> !}

B k b>0b0 y=kx+b (y=2x+1) I, III quarters y=kx+b (y=2x-1) I, III quarters y=kx I, III quarters Through the beginning of the coordinates K 0b0 y=kx+b (y=2x+1) I, III quarters y=kx+b (y=2x-1) I, III quarters y=kx I, III quarters Through the beginning of the coordinates K"> 0b0 y=kx +b (y=2x+1) I, III quarters y=kx+b (y=2x-1) I, III quarters y=kx I, III quarters Through the beginning of the coordinates K"> 0b0 y=kx+b (y =2x+1) I, III quarters y=kx+b (y=2x-1) I, III quarters y=kx I, III quarters Through the beginning of the coordinate K" title="(!LANG:b k b>0b0 y=kx +b (y=2x+1) I, III quarters y=kx+b (y=2x-1) I, III quarters y=kx I, III quarters Through the origin of coordinates K"> title="b k b>0b0 y=kx+b (y=2x+1) I, III quarters y=kx+b (y=2x-1) I, III quarters y=kx I, III quarters Through the origin of coordinates K"> !}

B k b>0b0 y=kx+b (y=2x+1) I, III quad. y=kx+b (y=2x-1) I, III quarter. y=kx I, III quarters Through the beginning of the coordinates K 0b0 y=kx+b (y=2x+1) I, III quad. y=kx+b (y=2x-1) I, III quarter. y=kx I, III quarter Through the beginning of the coordinates K"> 0b0 y=kx+b (y=2x+1) I, III quarter y=kx+b (y=2x-1) I, III quarter y= kx I, III quarters Through the beginning of the coordinates K "> 0b0 y \u003d kx + b (y \u003d 2x + 1) I, III quarters. y=kx+b (y=2x-1) I, III quarter. y=kx I, III quarters Through the beginning of the coordinates K" title="(!LANG:b k b>0b0 y=kx+b (y=2x+1) I, III quarters y=kx+b (y=2x-1 ) I, III quarters y=kx I, III quarters Through the beginning of the coordinates K"> title="b k b>0b0 y=kx+b (y=2x+1) I, III quad. y=kx+b (y=2x-1) I, III quarter. y=kx I, III quarters Through the beginning of the coordinates K"> !}

Back forward

Attention! The slide preview is for informational purposes only and may not represent the full extent of the presentation. If you are interested this work please download the full version.

Members: 8th grade remedial school(or 7th grade of a comprehensive school).

Lesson time: 1 academic hour (35 minutes).

Lesson Objectives:

Consolidate knowledge and skills on the topic "Function y=kx";
Learn to plot a linear function;
To develop the desire for independent research activities;
Continue to develop the ability to work with drawing tools (ruler).

Lesson objectives:

Conduct a comparative analysis of the functions y=kx and y=kx+b;
To introduce students to the concept of "Linear function" and its graph;

Equipment for the lesson:

Textbook Sh.A. Alimov "Algebra 7";
Presentation on the topic "Linear function and its graph";
A computer;
Touch screen;
Cards with images of graphs of functions y=2x and y= – 2x ( Attachment 1);
Cards with tasks for plotting a graph of a linear function ( application 2);
Rectangular coordinate system card ( appendix 3);
Cards for the research work "Similarities and differences" ( annex 4);
Linear function definition card ( annex 5).

Lesson plan:

Organizational moment - 2 minutes;
Updating knowledge - 5 min;
Explanation of new material - 15 min;
Problem solving - 10 min;
Summing up the lesson - 2 min;
Homework- 1 minute.

During the classes

I. Organizational moment

Checking compliance with the orthopedic regimen of students; recording the date of the lesson, the topic of the lesson; familiarization of students with the goals and objectives of the lesson.

II. Knowledge update

Exercise 1: Plot the function y=2x.

To complete the task, students with a severe degree of damage to the musculoskeletal system should be given a card "Rectangular coordinate system".

If the students fail to complete the task, review the task with the students.

Job analysis:

This function refers to the function y=kx. What object is the graph of this function?
Through how many points can a straight line be uniquely drawn?
This means that in order to graph the function y=2x, it is necessary to plot two points in the coordinate system that belong to this function. How to find the coordinates of a point that belongs to the graph with a given function formula?

After the analysis, students independently build a graph.

Task 2: Consider the properties of the constructed function.

Is this function increasing or decreasing?
Name the x values for which the function is positive.
Name the x values for which the function is negative.

So, we have repeated the plotting of the function y=kx and its properties. Today we will get acquainted with another kind of function, which is related to the function y=kx. We will conduct a comparative analysis of the two functions to find out their relationship. If someone is the first to see similarities and differences, draw conclusions, write them down on a card (issue a “Similarities and Differences” card).

III. Explanation of new material

A linear function is a function of the form y=kx+b, where k and b are given numbers. (slide 2)

Task 3: Functions are written on the board. Name the coefficients k and b in the linear functions indicated on the board (Figure 1):

Task 4: verbally complete 579 on page 140. Students take turns calling a function and giving a detailed answer to the question.

y=-x-2 is a linear function. The coefficient in front of x is -2, the free term is -2.
y=2x2+3 is not a linear function because x is to the second power.
y=x/3- is a linear function, since the coefficient in front of x is 1/3, the free term is 0. Teacher's help in case of difficulty: what number is the independent variable x multiplied by, if written x/3=x*1/3 ? What is the free term equal to if it is not in the entry?
y=250 - is a linear function, since the coefficient in front of x is 0, the free term is 250. Teacher help in case of difficulty: by what number can the independent variable x be multiplied if the product kx is missing?
y=3/x+8 - is not a linear function, since division by x is performed, not multiplication. Teacher help in case of difficulty: When multiplying a fraction by a number, is this number multiplied by the numerator or denominator?
y=-x/5+1 - is a linear function, since the coefficient in front of x is 1/5, the free term is 1. Teacher help in case of difficulty: When multiplying a fraction by a number, is this number multiplied by the numerator or denominator?

Let's continue studying the linear function.

Let us show that the graph of a linear function, as well as the graph of the function y=kx, is a straight line. To do this, we set a linear function, for example, y=x+1, in the form of a table for a certain number of points.

So, the function is given by the formula y=x+1. What are the coefficient k and the free term b of this function? What is the independent variable?

We will take arbitrary values of the independent variable x, located close to each other on the coordinate axis:

x	-2,5	-2	-1,5	-1	-0,5	0	0,5	1	1,5	2	2,5
y	-1,5	-1	-0,5	0	0,5	1	1,5	2	2,5	3	3,5

Let's build the found points in the coordinate system (click with the mouse to display the coordinate system). We mark the points we found (click with the mouse to plot the found points). Let's connect the constructed points (click with the mouse to build a straight line). It really is a straight line. If necessary, you can continue to choose the values of the independent variable to obtain a more accurate fit.

So, the graph of a linear function is a straight line (slide 3).

How many points are enough to construct so that a straight line can be uniquely drawn through them?

So, to build a graph of a linear function, it is enough (click with the mouse for the algorithm to appear):

choose two convenient values of the independent variable x;
find the value of the function from the selected x values;
Mark the found points on the coordinate plane;
Draw a line through the constructed points.

Task 5: in the rectangular coordinate system built for task 1, plot the function graph: y=2x+5, y=2x+3, y=2x-4, y=2x-2, y=2x+1. Give students cards with tasks (Appendix 3). Each student builds one of the functions (at the discretion of the teacher). When building a graph, try to independently answer the questions of the “Similarities and Differences” card.

Let's check the graphs of functions you built (slide 4). First, students name their chosen points.

We build a graph of the function y=2x+5 (click with the mouse): take convenient points (-2; 1) and (0; 5), draw a straight line through them (click with the mouse).

We build a graph of the function y=2x+3 (click with the mouse): take convenient points (0;3) and (1;5), draw a straight line through them (click with the mouse).

We build a graph of the function y=2x+1 (click with the mouse): take convenient points (0;1) and (1;3), draw a straight line through them (click with the mouse).

We build a graph of the function y=2x-2 (click with the mouse): take convenient points (0;-2) and (1;0), draw a straight line through them (click with the mouse).

We build a graph of the function y=2x-4 (click with the mouse): take convenient points (0;-4) and (2;0), draw a straight line through them (click with the mouse).

Previously, you plotted the function y=2x (click). Now each of you has built one more graph y=2x+5, y=2x+3, y=2x-4, y=2x-2, y=2x+1.

Last opportunity to fill in the Similarities and Differences cards yourself.

What is common between the formulas of the linear functions you have constructed? After receiving the answer, click the mouse.

How did the similarity appear on their graphs? After receiving the answer, click the mouse.

Why did it happen? What is the coefficient k for?

Each of the constructed functions has k=2, therefore the angles between the graphs and the Ox axis are equal, which means that the lines are parallel (click with the mouse).

What is the difference between the formulas of the constructed linear functions? After receiving the answer, click the mouse.

How did the difference show up on their charts? After receiving the answer, click the mouse to display the coefficient b of each function and display it on the graph.

What do you think free member b is responsible for?

What conclusion can you draw? How are the graphs of the functions y=kx and y=kx+b related.

the graph of the function y=kx+b is obtained by shifting the graph of the function y=kx by b units along the y-axis (slide 5);
the graphs of functions with the same values of the coefficient k are parallel straight lines.

Consider other examples:

The graphs of the functions y=-1/2x+1 and y=-1/2x (click) are parallel. One from the other is obtained by shifting by one unit along the Oy axis.
The graphs of the functions y=3x-5 and y=3x (click) are parallel. One from the other is obtained by a shift of five units along the Oy axis.
The graphs of the functions y=-3/7x-3 and y=-3/7x (click) are parallel. One from the other is obtained by shifting by three units along the Oy axis.

After summarizing the results of the comparison, fill in the cards "Similarities and differences". Provide individual assistance to students as needed.

IV. Problem solving

Task 6: build a rectangular coordinate system with a unit segment equal to two cells of the notebook. In the coordinate system, build the graphs of the functions indicated in 581. For students with a severe degree of damage to the musculoskeletal system, issue a ready-made coordinate system.

V. Summing up the lesson

What function did you meet today? After receiving the answer, click the mouse and say the definition of the linear function again.

What object is the graph of a linear function? After receiving the answer, click the mouse and once again say the method of plotting a linear function graph.

How are the graphs of the functions y=kx+b and y=kx related? After receiving the answer, click the mouse and say again the similarities and differences between the functions y=kx and y=kx+b.

VI. Homework

Know the definition of a linear function, 582 - to plot a linear function graph and to determine the values of variables x and y from the graph, 589 (orally) - give a full answer to the question (with explanation).

Thank you for the lesson(slide 7) !

Full name of the educational institution:

Municipal educational institution secondary school No. 3 of the village of Kochubeevskoye, Stavropol Territory

Subject area: mathematics

Lesson title: "Linear function, its schedule, properties.

Age group: 7th grade

Presentation title:Linear function, its graph, properties.

Number of slides: 37

Environment (editor) in which the presentation was made: Power Point 2010

This presentation

1 slide - title

2 slide-actualization of reference knowledge: definition of a linear equation, orally choose those that are linear from those proposed.

3 slide definition of a linear function.

4 slide recognition of a linear function from the proposed ones.

5 slide output.

6 slide ways to set the function.

7 slide-I give an example, I show.

8 slide - I give an example, I show.

9 slide task for students.

10 slide - checking the correctness of the task. I draw the attention of students to the relationship between the coefficients k and b and the location of the graphs.

11 slide conclusion.

12 slide - work with a graph of a linear function.

13 slide tasks for independent decision: construct graphs of functions (perform in a notebook).

14-17 slides show the correct execution of the task.

18-27 slides - oral and written assignments. I do not choose all tasks, but only those that are suitable for the level of preparedness of the classif there is time.

28 slide task for strong students.

29 slides - let's summarize.

30-31 slides - conclusions.

32-36 slides - historical background. (if there is time)

37 slide-Used literature

List of used literature and Internet resources:

1. Mordkovich A.G. and others. Algebra: a textbook for the 7th grade of educational institutions - M.: Education, 2010.

2. Zvavich L.I. and etc. Didactic materials in algebra for grade 7 - M.: Enlightenment, 2010.

3. Algebra grade 7, edited by Makarychev Yu.N. et al., Education, 2010

4. Internet resources:www.symbolsbook.ru/Article.aspx%...id%3D222

Preview:

To use the preview of presentations, create a Google account (account) and sign in: https://accounts.google.com

Slides captions:

Linear function, its graph, properties. Kiryanova Marina Vladimirovna, teacher of mathematics, secondary school No. 3 p. Kochubeevskoye, Stavropol Territory

Specify linear equations: 1) 5y = x 2) 3y = 0 3) y 2 + 16x 2 = 0 4) + y = 4 5) x + y =4 6) y = -x + 11 7) + 0.5x – 2 = 0 8) 25d - 2m + 1 = 0 9) y = 3 - 2x 5

A function of the form y = kx + b is called linear. The graph of a function of the form y = kx +b is a straight line. Only two points are needed to construct a line, since only one line passes through two points.

Find equations of linear functions y =-x+0.2; y=12, 4x-5.7; y =- 9 x- 1 8; y=5.04x; y=-5.04x; y=1 26.35+ 8.75x; y=x -0, 2; y=x:8; y=0.005x; y=13 3 ,13 3 13 3 x; y= 3 - 10 , 01x ; y=2: x ; y=-0.0049; y= x:6 2 .

y \u003d kx + b - linear function x - argument (independent variable) y - function (dependent variable) k , b - numbers (coefficients) k ≠ 0

x x 1 x 2 x 3 y y 1 y 2 y 3

y \u003d - 2x + 3 is a linear function. The graph of a linear function is a straight line, to build a straight line, you need to have two points x - an independent variable, so we will choose its values ourselves; Y is a dependent variable, its value will be obtained by substituting the selected x value into the function. We write the results in the table: x y 0 2 If x \u003d 0, then y \u003d - 2 0 + 3 \u003d 3. 3 If x=2, then y = -2 2+3 = - 4+3= -1. - 1 Mark the points (0;3) and (2; -1) on the coordinate plane and draw a straight line through them. x y 0 1 1 Y \u003d - 2x + 3 3 2 - 1 we choose ourselves

Construct a graph of a linear function y \u003d - 2 x +3 Compose a table: x y 03 1 1 Construct points (0; 3) and (1; 5) on the coordinate plane and draw a line x 1 0 1 3 y through them

Option I Option II y=x-4 y =- x+4 Determine the relationship between the coefficients k and b and the location of the lines Draw a graph of a linear function

y=x-4 y=-x+4 I option II option x y 1 2 0 -4 x 1 2 0 4 y

x 0 y y = kx + m (k > 0) x 0 y y = kx + m (k 0, then the linear function y = kx + b increases if k

Using the graph of a linear function y \u003d 2x - 6, answer the questions: a) at what value of x will y \u003d 0? b) for what values of x will y  0? c) for what values of x will y  0? 1 0 3 y 1 x -6 a) y \u003d 0 for x \u003d 3 b) y  0 for x  3 at x  3 If x  3, then the line is located below the x-axis, which means that the ordinates of the corresponding points of the line are negative

Tasks for independent solution: build graphs of functions (perform in a notebook) 1. y \u003d 2x - 2 2. y \u003d x + 2 3. y \u003d 4 - x 4. y \u003d 1 - 3x Please note: the points you have chosen to build a straight line may be different, but the location of the graphs must necessarily match

Answer to task 1

Answer to task 2

Answer to task 3

Answer to task 4

Which figure shows the graph of a linear function y = kx ? Explain answer. 1 2 3 4 5 x y x y x y x y x y

The student made a mistake while plotting the function graph. In what picture? 1. y \u003d x + 2 2. y \u003d 1.5 x 3. y \u003d -x-1 x y 2 1 x y 3 1 x y 3 3

1 2 3 4 5 x y x y y x y x y In which figure is coefficient k negative? x

What is the sign of the coefficient k for each of the linear functions:

In which figure is the free term b in the equation of a linear function negative? 1 2 3 4 5 x y x y x y x y x y

Choose a linear function whose graph is shown in the figure y = x - 2 y = x + 2 y = 2 - x y = x - 1 y = - x + 1 y = - x - 1 y = 0.5x y = x + 2 y \u003d 2x Well done! Think!

x y 1 2 0 1 2 3 -1 -2 -1 -2 x y 1 2 0 1 2 3 -1 -2 -1 -2 y=2x y=2x+ 1 y=2x- 1 y=-2x+ 1 y = - 2x-1y=-2x

y=-0.5x+ 2 , y=-0.5x , y=-0.5x- 2 x y 1 2 0 1 2 3 -1 -2 -1 -2 3 4 5 6 -3 x y 1 2 0 2 3 -1 -2 -1 -2 3 4 5 6 -3 1 y=0.5x+ 2 y=0.5x- 2 y=0.5x y=-0.5x+ 2 y=-0.5x y=-0 .5x-2

y=x+ 1 y=x- 1 , y=x y 1 2 0 1 2 3 -1 -2 -1 -2 3 4 5 6 -3 x y 1 2 0 1 2 3 -1 -2 -1 -2 3 4 5 6 -3 x y=-x y=-x+ 3 y=-x- 3 y=x+ 1 y=x- 1 y=x

Write an equation for a linear function according to the following conditions:

summarize

Write the conclusions in a notebook We learned: * A function of the form y \u003d kx + b is called linear. * The graph of a function of the form y = kx + b is a straight line. *To draw a straight line, only two points are needed, since only one straight line passes through two points. *The k coefficient shows whether the line is increasing or decreasing. *Coefficient b shows at what point the line intersects the OY axis. *Condition of parallelism of two lines.

Wish you success!

Algebra - this word comes from the title of the work of Muhammad Al-Khwarizmi "Al-jebr and Al-muqabala", in which algebra was presented as an independent subject

Robert Record is an English mathematician who in 1556 introduced the equal sign and explained his choice by the fact that nothing can be more equal than two parallel segments.

Gottfried Leibniz - German mathematician (1646 - 1716), who first introduced the term "abscissa" - in 1695, "ordinate" - in 1684, "coordinates" - in 1692.

Rene Descartes - French philosopher and mathematician (1596 - 1650), who first introduced the concept of "function"

References 1. Mordkovich A.G. and others. Algebra: a textbook for the 7th grade of educational institutions - M .: Education, 2010. 2. Zvavich L.I. and others. Didactic materials on algebra for grade 7 - M .: Education, 2010. 3. Algebra grade 7, edited by Makarychev Yu.N. et al., Enlightenment, 2010 4. Internet resources: www.symbolsbook.ru/Article.aspx%...id%3D222

Deputy Director for UVR,

mathematic teacher

MOU "Secondary School No. 65 named after. B.P. Agapitov UIPMETS»

city of Magnitogorsk