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The intersection point of two lines

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

Two lines meet in one point (der Schnittpunkt). You read it off and calculate it: with the equating method (das Gleichsetzungsverfahren).
📄 Open worksheet (PDF, German)

The video

In the video we set two terms equal, solve for x and check. Then we compare two phone contracts.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:24 Setting equal
  3. 1:01 The check
  4. 1:16 Two phone contracts
  5. 2:03 Careful, mistake!
  6. 2:25 Try it yourself

The most important points

The equating method

\(x + 1 = -x + 5\) (set equal), \(2 \cdot x = 4\), \(x = 2\) (solve for x), \(y = 2 + 1 = 3\) (substitute). The intersection point is \(S(2\,|\,3)\).

Set equal, solve, substitute and check.
Set equal, solve, substitute and check.
Contract A and contract B cost the same at 50 minutes: 15 €.
Contract A and contract B cost the same at 50 minutes: 15 €.

A point has two coordinates. After \(x = 2\) you also calculate \(y\).

x = 2 alone is not yet the intersection point.
\(x = 2\) alone is not yet the intersection point.

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
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Try it yourself

Task

Calculate the intersection point of \(y = 2 \cdot x - 1\) and \(y = x + 2\).

Show solution

\(2 \cdot x - 1 = x + 2\), \(x = 3\), \(y = 3 + 2 = 5\): \(S(3\,|\,5)\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: den Schnittpunkt zweier Geraden (ablesen, Gleichsetzungsverfahren, Probe, Anwendung Handyverträge). 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.