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Linear Function

A linear function has the form f(x)=m⋅x+b. Its graph is a straight line.

General liner equation: f(x)=m⋅x+b

For example, the graph of a linear function f(x)=2x+4 looks like this:

lineare Funktion

The slope m

The number m in front of the variable x indicates the slope of the function.

The slope can be read from the graph using the gradient triangle:

m=ΔyΔx

In the example the slope is

m=ΔyΔx=42=2
Steigungsdreieck, Lineare Funktion

The y-axis intercept b

The number b indicates the y-axis intercept of the function. The y-axis intercept is the function value at x=0.

The function graph therefore intersects the y-axis at the point (0,b).

Often an n or a t is used instead of the b.

y-Achsenabschnitt einer Geraden

Examples

Graph einer linearen Funktion
Image
Graph einer linearen Funktion
Graph einer linearen Funktion
Graph einer linearen Funktion

Video on the topic "Linear functions"

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This video explains what is meant by a linear function.

  • For each x-value you get exactly one y-value.

  • The highest exponent of x is 1.

  • Example: y = 0.5x + 1 

The terms function equation and function graph are explained.

This video was created by Sebastian Schmidt for his lessons according to the Flipped Classroom concept and was published on his channel on YouTube.

It continues with function equations and zeros of linear functions. This work is available under the free licence CC BY-SA 4.0.Information.


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