RD Sharma Chapter 13 Class 9 Maths Exercise 13.4 Solutions is about the Equations of lines parallel to the x-axis and y-axis. Any point in the pattern(x, 0), where x is the real number, lies on the x-axis because the y-coordinate of every spot on the x-axis is zero. The equation of the x-axis is y= 0. Likewise, the equation of the y-axis is x= 0 as the x-coordinate of every spot on the y-axis is zero. Practicing questions based on the graph is comparatively from the other problems. Also, students can obtain the marks more easily as these questions get solved quickly. It is effortless to score well in the exam with the help of problems on graphs.
We have attached the RD Sharma Chapter 13 Class 9 Maths Exercise 13.4 Solutions PDF to practice with the various types of questions related to the x-axis and the y-axis. The PDF is prepared by our experts for the students in which the solutions of problems are provided in a stepwise and easy manner.
Learn about RD Sharma Chapter 13 (Linear Equations In Two Variables) Class 9
Download RD Sharma Chapter 13 Class 9 Maths Exercise 13.4 Solutions PDF
Solutions for Class 9 Maths Chapter 13 Linear Equations in Two Variables Exercise 13.4
Important Definitions RD Sharma Chapter 13 Class 9 Maths Exercise 13.4 Solutions
In the following points, we will discuss the Equation of a Line Parallel to the x-axis and the y-axis separately with definitions and examples.
Equation of a Line Parallel to the x-Axis
To obtain the equation of the x-axis and a line parallel to the x-axis-
Consider ‘AB’ to be a straight line parallel to the x-axis at the distance ‘b’ units from it. Then, all points on a line ‘AB’ have the corresponding ordinate ‘b’. Thus, ‘AB’ can be recognized as the locus of a point at a distance ‘b’ from the x-axis, and all points on a line ‘AB’ meet the condition y = b.
If P(x, y) in any position on ‘AB’, then y = b.
Consequently, the equation of a straight line parallels to the x-axis at a distance ‘b’ from it is y = b.
The equation of the x-axis is y = 0 since the x-axis is parallel to itself at a distance of ‘0’ from it.
Or
Let P(x,y) be any position on the x-axis. Simply, for all positions of ‘P’, we shall have the same ordinate 0 or y = 0.
Therefore, an equation of the x-axis is y = 0.
If a straight line is parallel and down to the x-axis at a distance ‘b,’ then the equation is y = -b.
Equation of a Line Parallel to the y-Axis
Here, we will study how to obtain the equation of the y-axis and an equation of a line parallel to the y-axis.
Consider ‘AB’ to be a straight line parallel to the y-axis at a distance ‘a’ units from it. Then, all points on a line AB have the same abscissa ‘a’. So, ‘AB’ can be recognized as the locus of the point at a distance ‘a’ from the y-axis, and all points on a line ‘AB’ meet the condition x = a.
If P(x, y) in any position on ‘AB’, then x = a.
Consequently, the equation of a straight line parallels to the y-axis at the distance ‘a’ from it is x = a.
The equation of the y-axis is x = 0 since the y-axis is the parallel to itself at a distance of ‘0’ from it.
Or
Let P (x, y) be any position on the y-axis. Then simply, for all positions of ‘P,’ we shall have the same abscissa 0 or, x = 0.
Accordingly, the equation of the y-axis is x = 0.
If a straight line is parallel and to the left of the x-axis at a distance ‘a’, then the equation is x = -a.
Examples related to the Equations of lines parallel to the x-axis and y-axis of RD Sharma Chapter 13 Class 9 Maths Exercise 13.4 Solutions
Ques 1- Find an equation of a straight line parallels to the x-axis at the distance of 10 units above the x-axis.
Ans- We know that an equation of a straight line parallel to the x-axis at a distance ‘b’ from it is y = b. Hence, an equation of a straight line parallels to the x-axis at a distance of 10 (ten) units above the x-axis is y = 10.
Ques 2- Find an equation of a straight line parallels to the y-axis at the distance of 3 units on the left-hand side of the y-axis.
Ans- We know that an equation of a straight line is parallel, and to the left of the x-axis at a distance ‘a’, then the equation is x = -a. Hence, an equation of the straight line parallel to the y-axis at the distance of 3 units on the left-hand side of the y-axis is x = -3.