Question 1:
Give the geometric representation of y = 3 as an equation
(i)in one variable
(ii)in two variables
Solution 1:
(i)Given,
y = 3 is the equation
The representation of the solution on the number when y = 3 is treated as an equation in one variable
In one variable, y = 3 represents a point as shown in following figure.
(ii)Given:
y = 3 is the equation
We know that y = 3 can be written as 0.x + y = 0 .
In two variables, y = 3 represents a straight line passing through point (0, 3) and parallel to x-axis. It is a collection of all points of the plane, having their y-coordinate as 3.
Hence,
When, x = 0, we get y = 3 ;
When x = 2, we get y = 3 ;
When x = - 2 , we get y = 3 are the solutions for the equations.
Plotting the points (0, 3) (2, 3) and (–2, 3) and on joining them we get the graph AB as a line parallel to x-axis at a distance of 3 units above it
The graphical representation is shown below: Exercise (4.4)
Question 2:
Give the geometric representations of 2x + 9 = 0 as an equation
(i)in one variable
(ii)in two variables
Solution 2:
(i)Given: 2x + 9 = 0 is the Linear Equation ------------ Equation (1)
2x +9 =0
2x = 9
x=-9/2=-4.5
Hence,in one variable 2x + 9 = 0 represents a point as shown in the following figure.
(ii)Given: 2x + 9 = 0 is the Linear Equation ------------ Equation (1)
We know that 2x + 9 = 0 can be written as 2x + 0y + 9 = 0 as a linear equation in variables x and y.
Value of y is always 0. However, x must satisfy the relation 2x + 9= 0
i.e.
x=-9/2=-4.5
Hence,
When, y= 0, we get x= -4.5 ;
When y = 2, we get x= -4.5;
When y = - 2, we get x= -4.5 are the solutions for the equations.
Hence three solution of the given equation are, y = 0 ; ,y = 2 and ,y =– 2.
Therefore, plotting the point and on joining them we get the graph AB as a line parallel to y-axis at a distance of on the left of y-axis It is a collection of all points of the plane, having their x-coordinate as 4.5.
