"Linear function and its image" PPT courseware 2

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"Linear function and its image" PPT courseware 2

review knowledge

1. The general form of a linear function is y=kx+b(k,b are constants, k≠0)

The general form of the proportional function is y=kx (k is a constant, k≠0)

What's the connection between the two? The proportional function is a special linear function

2. What are the general steps for drawing function images using the point tracing method?

List--Draw points--Connect lines

Discuss

(1) Can you find the abscissa of the intersection of the image of the linear function y=kx+b and the x-axis and the ordinate of the intersection of the image and the y-axis?

The abscissa is -k/b, the ordinate is b;

That is, when y=0, x=-k/b, when x=0, y=b.

(3) Yes (2) Did you find any relationship between the graph of the linear function y=kx+b and the abscissa of the intersection point of the x-axis and the solution of the linear equation kx+b=0?

(4) Given the linear function y=2x+4, can you draw its image using a relatively simple method? Communicate with classmates.

Taking x=0, we get y=4; taking y=0, we get x=-2. Draw a straight line through two points A(0,4) and B(-2,0). Straight line AB is the function y=2x+4 image.

(5) Generally speaking, what point do you think is easier to choose to draw the straight line y=kx+b (k≠0)? Draw a straight line y=kx (k≠0)

When drawing a straight line y=kx(k≠0), just find a point on the straight line that is not the origin and draw a straight line passing through this point and the origin.

practice

1. The straight line y=4x+2 passes through the points (0, 2) and (-1/2, 0).

2. The straight line y=-3x – 1 passes through the points (-1/3, 0) and (0, -1).

3. The coordinates of the intersection point of the straight line y=-2x-3 and the x-axis are ________ and the coordinates of the intersection point of the y-axis are ________

4. It is known that the graph of linear function y=(m-1)x+2m+1 passes through the origin, then m=________.

Improvement in perception

It is known that the graph of a linear function passes through points (3,5) and (-4,-9).

Find the analytical formula of this linear function.

Solution: Let the analytical formula of this linear function be y=kx+b.

The image of ∵y=kx+b passes through points (3, 5) and (-4, -9).

∴ 3k+b=5

-4k+b=-9

Solve for k=2

b=-1

∴The analytical formula of this linear function is y=2x-1

Summary

1. The general steps for drawing function images using the point drawing method are: list, point drawing, and connecting lines.

2. The image of the linear function y=kx+b (k and b are constants, and k≠0) is a straight line, so the image of the linear function y=kx+b is also called the straight line y=kx+b.

3. When drawing the image of a linear function, the two intersection points of the image and the coordinate axis are usually selected to determine the straight line. A proportional function is a straight line through the origin

4. Method to determine the analytical expression of a function: Undetermined coefficient method

Keywords: linear function and its image teaching courseware, Qingdao edition eighth grade mathematics volume PPT courseware download, eighth grade mathematics slide courseware download, linear function and its image PPT courseware download, .PPT format;

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Update Time: 2024-09-07

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