Give the geometric representation of 3x 1 x 5 as an equation in i one variable ii two variables

(i) If y = 3 is treated as an equation in one variable y only, then it has the unique solution y = 3, which is a point on the number line

(ii) When an equation in two variables, it can be expressed as,

0.x + y – 3 = 0

which is a linear equation in the variables x and y.

When x = 0, y = 3

When x = 1, y = 3

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Give geometrical representation of equation 3 x+12=0 in1 one variable 2two variables

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Solution:

(i) In one variable, y = 3 represents a point as shown in the following figure.

(ii) We know that y = 3 can be written as, 0x + y = 3

In two variables, y = 3 represents a straight line passing through the point (0, 3) and parallel to the x-axis. It is a collection of all the points on 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

Plotting the points (0, 3) (2, 3) and (-2, 3) and on joining them we get the graph AB as a line parallel to the x-axis at a distance of 3 units above it.

The graphical representation is shown below:

☛ Check: NCERT Solutions Class 9 Maths Chapter 4

Video Solution:

Give the geometric representations of y = 3 as an equation (i) in one variable (ii) in two variables

NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.4 Question 1

Summary:

In one variable, y = 3 represents a point and in two variables, y = 3 represents a straight line passing through the point (0, 3) and parallel to the x-axis.

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