Learning Graphic Methods

The different variables that govern a particular situation may be connected by an equation. Using the equation connected by two variables x and y we can get a value for y for each given value of x and get a set of ordered pair (x, y) of real numbers. All these ordered pairs (x, y) can be plotted as points in the Cartesian plane where the horizontal line represents x-axis and the vertical line represents y-axis. These points now define the graph.

 

Methods of learning graph:

 

Different Methods of plotting a graph :

1. Linear graph method

2. Quadratic graph method

Steps to learn the linear and quadratic graph methods:

Step 1: By substituting two different values for x in the equations y = mx + c, y=ax² + bx + c we get two values for y. Thus we get two points (x₁, y₁) and (x₂, y₂) on the line.

Step 2: Draw the x-axis and y-axis on the graph paper and choose a suitable scale on the co- ordinate axes. The scale for both the axes is chosen based on the values of the co-ordinates obtained in step 1. If the co-ordinate values are large, then 1 cm along the axes may be taken to represents large number of units.

Step 3: Plot the two points (x₁, y₁) and (x₂, y₂) in Cartesian plane of the paper.

Step 4: Join the two points by a line segment and extend it in both directions of the segment. This is the required graph.

I am planning to write more post on Multiplication of Decimals with example, Explain Histogram. Keep checking my blog.

 

Examples of graphic methods:

 

Ex 1: Draw the graph of the line y  =  2x.

Solution: The equation of the line is y  = 2x

Substituting x = −1, 0, 1, we get   y = -2, 0, 2. Plot the points (−1, -2), (0, 0) and (1,−1) in the graph paper

X    -1    0    1

Y    -2   0     2

(See the figure.1)

Figure . 1

Ex 2:Draw the graph of y  =  2x² – 5x +2.

Solution: Draw x-axis 1 cm = 1 unit and on y-axis 1 cm = 2 units. Assign values x = –4 to 5 and calculate the Corresponding y values.

X            0    1     2    3      4

X²         0    1     4     9     16

Y           2   -1     0      5      14

We plot the points (0,2), (1, –1), (2,0), (3,5),(4,14)on the graph sheet and join these points by a smooth curve.

(see the figure.2)

Figure . 2