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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.
☛ Related Questions:
Math worksheets and
visual curriculum
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:
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:
Math worksheets and
visual curriculum
Answer
Hint: Geometrically, each solution \[(x,y)\] of a linear equation in two variables, \[ax + by + c = 0\], where \[a,b,c\] are constants, corresponds to a point on the line representing the equation, and vice versa.The one variable, we represent in graphical by a line either \[x\] or \[y\]. In this sum we use \[y\] line to represent a one variable equation or single variable equation.The two variables, we represent in graphical by a line in \[xy - plane\].
Complete step-by-step answer:
It is given that the equation of the line is\[2y + 7 = 0\]We take the integer as LHS,\[2y = - 7....\left( 1 \right)\] Let us divided, \[y = - \dfrac{7}{2}\]\[y = - 3.5\]The equation \[y = - 3.5\] is called the one variable equation or single variable equationHence the equation \[y = - 3.5\] an equation of one variable That is $y$ as one variable.Now, A linear equation with two variables is of the form \[ax + by + c = 0\] where \[a, b, c\] is constant.To make the form, from the given equation That is \[2y + 7 = 0\]\[2y = - 7\]Here, \[x - {\text{variable}}\] is missing so that, we add \[0x + 2y = - 7\]Taking the integer to RHS,\[0x + 2y + 7 = 0\]So the values are,\[a = 0,b = 2,c = 7\]So that the point of the given equation has \[y = - 3.5\] and \[x = 0\] The graph can be plotted like this\[(x,y) = (0, - 3.5)\]We can plot these points in the Cartesian plane (two variable plane) or \[xy - plane\]
Note: The concept we use is the geometrical representation of linear equation
A one variable equation or single variable equation, a variable is a symbolic placeholder for a number we do not yet know. It’s very common to see \[x\]or \[y\]used as a variable in math problems.A single variable equation is an equation in which there is only one variable used.It is only a geometrical representation problem, we also solve it for graphical representation to understand the problem.