Plotting a Linear Equation On Graph


 
 
Concept Explanation
 

Plotting a Linear Equation On Graph

A linear equation in two variables has infinitely many solutions. We can plot these solutions on a graph. Each  solution represents a point on the graph, Let us take any three solutions  and plot them on the graph as P, Q and R, we will see that on joining these three points we get a straight line passing through them. We find that a linear equation in two variables is geometrically represented by a line such that:

(i)  Every solution of the linear equation represents a point on the line.

(ii) Every point on the line is a solution of the linear equation.

Illustration: Draw the graph of the equation y-x=2

Solution:  We will try to find three solutions for the linear equation,

                   y-x=2 ;; Rightarrow;;y=x+2

When x=1, we have : y=1+2=3

When x=3, we have : y=3+2=5

When large x=4, we have : y=4+2=6

Thus, we have the following table exhibiting the abscissae and ordinates of points on the line represented by the given equation

x 1 3 4
y 3 5 6

Plotting the points (1,3), (3,5) and (4,6) on the graph paper and drawing a line joining them , we obtain the graph of the line represented by the given equation

Sample Questions
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Question : 1

Any point on x-axis is of the form _________________

Right Option : A
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Question : 2

Choose the correct graph for the linear equation  y = 2x - 3  .

Right Option : C
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Explanation
Question : 3

How many linear equations when representing graphically pass through x=2 and y = -3

Right Option : D
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Explanation
 
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