"Looking at equations (groups) or inequalities from the perspective of functions" linear function PPT courseware 2

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"Looking at equations (groups) or inequalities from the perspective of functions" linear function PPT courseware 2

(1) Solve the equation: 2x+20=0

(2) When x has what value, the value of function y=2x+20 is 0?

What is the relationship between questions (1) and (2)?

From the function graph, the coordinates of the intersection of the straight line y=2x+20 and the x-axis are (-10, 0)

It shows that the solution of equation 2x+20=0 is x=-10

think

From the relationship between the above two questions, we can further obtain that when "solving the equation ax+b=0 (a, b is a constant, a≠0)" and finding the value of the independent variable x, the value of the linear function y=ax+b is 0" What does it matter?

Find the solution of ax+b=0 (a, b are constants, a≠0).

From the perspective of "number"

When x has a value, the value of function y= ax+b is 0.

Find the solution of ax+b=0 (a, b are constants, a≠0).

From the perspective of "form"

Find the abscissa coordinate of the intersection of the straight line y= ax+b and the x-axis.

practise

1. Can you directly tell the solution to the linear equation x+3=0 based on the picture?

Solution: It can be seen from the image that the solution of x+3=0 is x = −3.

2. Use the graph of the function to solve for x: 5x-1=2x+5

Solution 1: Transform the equation 5x−1=2x+5 into 3x−6=0,

Draw the graph of the function y=3x −6.

It can be seen from the image that the intersection point of the straight line y=3x −6 and the x-axis is (2,0), so the solution of the original equation is x=2.

Solution 2: Draw the graphs of the two functions y=5x−1 and y=2x+5

From the image, we know that the two straight lines intersect at point (2, 9), so the solution of the original equation is x=2.

reward

Solving the linear equation ax+b=0 (a, b is a constant) can be transformed into: when the value of a linear function is 0, find the value of the corresponding independent variable. Graphically, this is equivalent to knowing the straight line y=ax+b and determining the value of the abscissa of its intersection with the x-axis.

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For more information about the PPT courseware "Linear Functions: Viewing Equations (Groups) or Inequalities from the Perspective of Functions", please click the "Linear Functions ppt Viewing Equations (Groups) or Inequalities from the Perspective of Functions" ppt tag.

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"Looking at equations (groups) or inequalities from the perspective of functions" PPT courseware for linear functions:

"Looking at equations (groups) or inequalities from the perspective of functions" PPT courseware on linear functions Observation What is the relationship between the following two questions? (1) Solve the equation 2x+20=0 (2) When the independent variable x is what value, the value of the function y =2x+20 is 0? Solution: (1) 2x+20=0 (2) ..

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Update Time: 2024-11-08

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 2 industry PPT template

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