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Linear functions

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

Not every straight line goes through the zero point. There is one equation for all lines: \(y = m \cdot x + b\) (die lineare Funktion).
📄 Open worksheet (PDF, German)

The video

In the video we calculate a table of values, draw the line and read off the slope and the y-intercept.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:26 Table of values and graph
  3. 1:04 The y-intercept
  4. 1:18 The slope
  5. 1:48 Falling lines
  6. 2:10 Careful, mistake!
  7. 2:33 Try it yourself

The most important points

y = m · x + b

m is the slope (die Steigung): 1 to the right, then \(m\) up (slope triangle, das Steigungsdreieck). b is the y-intercept (der y-Achsenabschnitt): there the line crosses the y-axis.

y = 2 · x + 1: b = 1 and m = 2.
\(y = 2 \cdot x + 1\): \(b = 1\) and \(m = 2\).

If \(m\) is negative, the line falls: \(y = -2 \cdot x + 5\) goes 1 to the right and 2 down.

A falling line with m = -2 and b = 5.
A falling line with \(m = -2\) and \(b = 5\).
y = 3 · x + 2 crosses the y-axis at 2, not at 3.
\(y = 3 \cdot x + 2\) crosses the y-axis at 2, not at 3.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

What are \(m\) and \(b\)? a) \(y = 4 \cdot x - 3\) b) \(y = -x + 2\)

Show solution

a) \(m = 4\), \(b = -3\) b) \(m = -1\), \(b = 2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: lineare Funktionen y = m·x + b (Steigung, Steigungsdreieck, y-Achsenabschnitt, steigende und fallende Geraden). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.