Some Applications

13.2 Some Applications

Description

Quick Overview

This section explores the relationship between independent and dependent variables through practical applications, such as the correlation between electricity consumption and billing.

Standard

In this section, we discuss how certain quantities, such as electricity usage and its corresponding bill, exemplify the relationship between independent and dependent variables. The section features examples, graph plotting, and concepts such as linear relationships and direct variation.

Detailed

In this section, we highlight several applications of graphs in everyday situations. The section opens with a discussion on how utility expenses, such as electricity bills, relate to the quantities consumed, identifying the independent variable (amount of electricity used) and the dependent variable (the resulting bill). Through engaging examples, such as the cost of petrol and banking interests, students learn to plot linear graphs representing direct relationships. Each example emphasizes how linear graphs can illustrate data trends, allowing for better comprehension. The section concludes with practice exercises and concepts reinforcing understanding of how to analyze and interpret relationships through graphical data representation.

Key Concepts

  • Independent Variable: The factor that is controlled or manipulated.

  • Dependent Variable: The outcome that depends on the independent variable.

  • Linear Relationship: A relationship that can be represented by a straight line on a graph.

  • Direct Variation: When one variable directly affects another in a proportional manner.

Memory Aids

🎵 Rhymes Time

  • Independent stays in control, dependent follows the goal.

📖 Fascinating Stories

  • Imagine a tree; the sun (independent) determines how much fruit (dependent) it grows.

🧠 Other Memory Gems

  • DAD - Dependent Affects Dependent.

🎯 Super Acronyms

GRA - Graphs Reflect Applications.

Examples

  • In the relationship between electricity usage and billing, more electricity consumed results in higher bills.

  • The cost of petrol increases linearly with the number of litres purchased.

  • In simple interest calculations, the interest earned is directly proportional to the amount deposited.

Glossary of Terms

  • Term: Independent Variable

    Definition:

    The variable that is manipulated or controlled in an experiment.

  • Term: Dependent Variable

    Definition:

    The variable that is measured or affected in an experiment.

  • Term: Linear Graph

    Definition:

    A graph that represents a straight line, indicating a direct relationship between two variables.

  • Term: Direct Variation

    Definition:

    A relationship between two variables where they increase or decrease together.

  • Term: Graph

    Definition:

    A visual representation of data and relationships between variables.