Give the geometric representations of 2x + 9 = 0 as an equation
(i) in one variable
(ii) in two variables

Solution:

(i) 2x + 9 = 0

2x = - 9

x = - 9/2

x = - 4.5

Hence, in one variable 2x + 9 = 0 represents a point as shown in the following figure.

(ii) We know that 2x + 9 = 0 can be written as 2x + 0y + 9 = 0 as a linear equation in two 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 

Therefore, plotting the points and on joining them we get the graph AB as a line parallel to the y-axis at a distance of 4.5 units on the left of the y-axis. It is a collection of all points of the plane, having their x-coordinate as 4.5.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 4

Video Solution:

Give the geometric representations of 2x + 9 = 0 as an equation (i) in one variable (ii) in two variables

NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.4 Question 2

Summary:

In one variable, 2x + 9 = 0 represents a point and in two variables, 2x + 9 = 0 represents a straight line passing through the point (- 9/2, 0) and parallel to the y-axis.

☛ Related Questions:

• Yamini and Fatima, two students of Class IX of a school, together contributed '100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as 'x and 'y.) Draw the graph of the same.
• In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius: F = (9/5)C + 32 i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis. ii) If the temperature is 30o C, what is the temperature in Fahrenheit? iii) If the temperature is 95o F, what is the temperature in Celsius? iv) If the temperature is 0o C, what is the temperature in Fahrenheit and if the temperature is 0o F, what is the temperature in Celsius?
• Give the geometric representation of y = 3 as an equation(i) in one variable(ii) in two variables