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Understanding gradients and areas in applied graphs

Algebra • Graphs

Key concepts

What you'll likely be quizzed about

  • The gradient of a line measures the steepness of the line, indicating how the dependent variable changes for each unit change in the independent variable.
  • It is calculated as the rise over run, represented mathematically as (change in y) / (change in x).
  • A positive gradient indicates a direct relationship, while a negative gradient shows an inverse relationship.
  • Understanding the gradient helps in predicting outcomes based on linear relationships.

Flashcards

Test your knowledge with interactive flashcards

Explain how to determine the area of a trapezium.

Click to reveal answer

The area is calculated by averaging the lengths of the parallel sides and multiplying by the height: Area = 0.5 * (a + b) * height.

Key notes

Important points to keep in mind

Gradient = rise/run

Area under a curve represents total value

Estimate areas using counting techniques

Positive gradient = direct relationship

Negative gradient = inverse relationship

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