Introduction to Graphs

Quick Revision Notes: Introduction to Graphs

Class 8 Mathematics (MP Board)

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### 1. Introduction to Graphs (आलेखों से परिचय)

A graph is a visual representation of data or information using a diagram, chart, or grid. It helps us understand the relationship between two quantities or variables easily.

• Data (आँकड़े): Collection of numbers gathered to give some information.
• Variable (चर): A quantity that can change or vary (e.g., time, temperature, distance).

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### 2. Coordinates and Cartesian System (निर्देशांक और कार्तीय पद्धति)

To locate a point on a graph paper, we use a system of two perpendicular number lines:

1. X-axis (क्षैतिज अक्ष): The horizontal number line.
2. Y-axis (ऊर्ध्वाधर अक्ष): The vertical number line.
3. Origin (मूलबिंदु): The point of intersection of the X-axis and Y-axis, denoted by $(0, 0)$.
4. Coordinates (निर्देशांक): A pair of numbers $(x, y)$ that locate a specific point on the graph.
   • X-coordinate / Abscissa ($x$): The horizontal distance from the origin.
   • Y-coordinate / Ordinate ($y$): The vertical distance from the origin.

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### 3. Types of Graphs (आलेखों کے प्रकार)

A. Bar Graph (दण्ड आलेख)

• Used to show comparisons among discrete categories using rectangular bars of uniform width.

B. Pie Chart / Circle Graph (वृत्त आलेख)

• Used to compare parts of a whole. The entire circle represents $360^\circ$ or $100%$.

C. Histogram (आयतचित्र)

• A bar graph used for continuous data grouped in intervals (class intervals) with no gaps between bars.

D. Line Graph (रेखीय आलेख)

• A graph that displays data that changes continuously over periods of time. Points are connected by line segments.

E. Linear Graph (रैखिक आलेख)

• A line graph that is a straight line.

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### 4. Reading a Line Graph (रेखीय आलेख को पढ़ना)

• To find the value of a variable at a specific time, locate that time on the X-axis, move vertically to the line/point, and then look horizontally at the Y-axis to read the corresponding value.
• Trend Analysis:
  • If the line goes upward from left to right, the value is increasing.
  • If the line goes downward from left to right, the value is decreasing.
  • If the line is horizontal, the value remains constant.

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### 5. Important Terms & Formulas for Problems

• Coordinates of a Point: Written as (x, y). Always write the $x$-coordinate first, followed by the $y$-coordinate.
• Scale Selection: Choosing the correct unit on the axes (e.g., 1 cm = 5 units) is crucial for drawing an accurate and neat graph.
• Direct Proportion (सीधा समानुपात): When two quantities, $x$ and $y$, increase or decrease together such that the ratio x / y = k (where $k$ is constant), their graph is always a straight line passing through the origin.