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Graph Of Linear Equation In Two Variable

Graph of Linear Equation In Two Variable Online Tutoring / Homework Help
This is a well-known fact that a linear equation has infinitely many solutions. And the solutions are written as pairs of values.

For example, the solution of the linear equation in two variables x + 2y = 6 can be expressed in the form of a table as given below:

x 2 0 6 4 ...
y 2 3 0 1 ...

On a graph paper these points (2, 2), (0, 3), (6, 0) and (4, 1) are plotted. Now if any two points are joined, a straight line AB is obtained. Hence the geometrical representation of equation x + 2y = 6 is a straight line.

Graph of Linear Equation In Two Variable Online Tutoring / Homework Help

All the points which lie on the line AB satisfy the equation x + 2y = 6. For example, if we take points (6, 0), (2, 2) then,

6 + 2(0) = 6 and 2 + 2(2) = 2 + 4 = 6 which means both the points satisfy the equation x + 2y = 6. Hence, (6, 0) and (2, 2) both are solutions of equation x + 2y = 6.

Now if we take a point (2, 0) which does not lie on the line AB then,

2 + 2(0) = 2 ≠ 6, i.e. the point (2, 0) does not satisfy the above equation. Hence, (2, 0) is not a solution.

Example 1:

Draw the graph of linear equation x y = 2.

Solution:

x y = 2    =>    y = x 2

Table of Solutions

x 2 3
y 0 1

Now plotting the points (2, 0) and (3, 1) on the graph paper and joining these with the help of a ruler we get the line which is the graph of the equation x y = 2.
Graph of Linear Equation In Two Variable Online Tutoring / Homework Help


Example 2:

If the point (1, 1) lies on the graph of the equation 6x + 2ay = 3a, find the value of a.

Solution:

If the point (1, 1) lies on the graph of the equation 6x + 2ay = 3a, then

6(1) + 2a(1) = 3a => 6 + 2a = 3a
=> 3a 2a = 6
=> a = 6      (Answer)


Example 3:

Draw the graph of equation 2x + 5y = 13 and check whether x = 2, y = 5 is a solution.

Solution:

2x + 5y = 13 => 5y = 13 2x
=> y = (13 - 2x)
            5
Table of Solutions

x -1 4
y 3 1

Now plotting the points (-1, 3) and (4, 1) on the graph paper and joining these with the help of a ruler we get the line which is the graph of the equation 2x + 5y = 13.
Graph of Linear Equation In Two Variable Online Tutoring / Homework Help
In the above representation, we can clearly see that the point (2, 5) does not lie on the graph and hence x = 2, y = 5 is not a solution of the given equation.

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