Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 ↓


Introduction to Graphs


Graphs are a visual representation of data. They help us understand data easily using pictures. When you hear the word "graph," you may think of bar graphs, pie charts, or line graphs. In math, especially in grade 8, we focus on line graphs and coordinate graphs, which help us see relationships between numbers. In this guide, we'll explore what graphs are, how they're used, and what types of graphs you may encounter.

What is a graph?

A graph is a picture that shows data in a way that is easy to understand. It helps us see patterns, relationships, and trends in data. For example, if you want to see how your grades change over a year, a graph can show you this quickly and easily.

Types of graphs

There are many types of graphs, but the most common graphs you will see in Class 8 are:

  • Bar graph
  • Line drawing
  • Coordinate graphs
  • Pie charts

Bar graph

Bar graphs use bars to represent numbers, such as how many people like different types of ice cream.

Vanilla Chocolate Strawberry

In this example, you can see that vanilla has the highest rating, meaning it is the most popular ice cream.

Line drawing

A line graph shows information as a series of data points called 'markers' that are connected by straight lines. Line graphs are useful for showing trends over time.

This line graph shows a simple trend where the data points follow a path in a grid. You can visualize this as the change in temperature over four days.

Coordinate graphs

Coordinate graphs use pairs of numbers to show positions. These numbers are known as coordinates and are usually written as (x, y).

(2, 2) (4, 4)

This example shows two points on a coordinate graph.

Understanding the coordinate plane

The coordinate plane is a two-dimensional surface on which you can draw points, lines, and curves. It is formed by two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical). These axes divide the plane into four parts called quadrants.

Every point on the coordinate plane has two numbers: an x-coordinate and a y-coordinate. These numbers are called coordinates. They are usually written in parentheses, such as: (x, y).

Example of coordinates

If you have a point (3, 4), that means you moved forward 3 places on the x-axis and up 4 places on the y-axis.

(3, 4)

You can imagine the coordinate plane as a map with directions, where each point is located using two sets of numbers.

Linear graphs

Linear graphs are one of the most basic and important forms of graphs that you will learn in Class 8. As the name suggests, they consist of lines.

The equation of a line is usually written in the form y = mx + c, where:

  • y is the value on the y-axis.
  • x is the value on the x-axis.
  • m is the slope of the line, which indicates how steep the line is.
  • c is the y-intercept, the point where the line intersects the y-axis.

Example of a linear equation

Consider the equation y = 2x + 1 You can plot it like this:

Create a table of values:

x|y
,
0 | 1
1 | 3
2 | 5
(0, 1) (1, 3) (2, 5)

It is a graphical representation of a line where each marked point satisfies the equation y = 2x + 1.

Understanding slope

The slope m of a line is a measure of its slope. It shows the relationship between a change in y and a change in x.

For example, if the slope m = 2, then for every 1 unit move forward along x, you move 2 units up along y.

Why are graphs important?

Graphs can make complex information easier to understand. By visually presenting data, graphs can quickly illustrate how different values are related. Here are some reasons why graphs are important:

  • Comparison: Graphs allow easy comparison of data sets.
  • Trends: They help identify trends and patterns over time.
  • Decision making: Visual data can help make informed decisions.
  • Communication: Graphs make it easier to communicate information clearly.

Practice problem

To test your understanding of graphs, try drawing the following line on a coordinate graph:

Equation: y = 3x - 2

Phase:

  • Make a table of the values of x and y.
  • Choose some x values, substitute into the equation to find y.
    • x|y
,
0 | -2
1 | 1
2 | 4
  • Plot these points on the graph.
  • Draw a line through the points to see a linear relationship.

Conclusion

Learning to read and understand graphs is a basic skill in math that will help you in a variety of topics and real-life situations. To fully understand graphs, it is important to plot different equations and examine how data sets relate to one another. Experimenting with different types of graphs will enhance your ability to visualize and solve problems efficiently.


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Introduction to Graphs

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