Equations Of Lines Parallel To The X-Axis And Y-Axis

On Sep 10, 2016

Equations Of Lines Parallel To The X-Axis And Y-Axis

We can represent graph of these equations in two types of geometrically

(A) in one variable or on number line

(B) in two variable or on the Cartesian plane

In one variable, the solution is represent by a point. While in two variable, the solution is represent by a line parallel to x or y axis.

Equations Of Lines Parallel To The X-Axis And Y-Axis Example Problems With Solutions

Example 1: Give the geometric representation of x = 5 as an equation in

(i) one variable

(ii) two variable

(iii) also find the common solution of x = 5 & x = 0

Solution: (i) x = 5

It is in only one variable so representation on number line

Equations-Of-Lines-Parallel-To-The-X-Axis-And-Y-Axis-Example-1

(ii) In two variables (or on Cartesian plane)

first we have to represent equation in two variables x + 0.y = 5 …..(i)

now we have to find two or three solutions of equations (i)

x	5	5	5
y	0	1	2

Then mark these points on graph with proper scale & join them

Equations-Of-Lines-Parallel-To-The-X-Axis-And-Y-Axis-Example-1-1

Scale: on both axis 10 lines or 1 big box = 1 cm

(iii) ∵ x = 5 is line parallel to y axis and x = 0 is y axis.

∴ both are parallel

∴ no common solution

Example 2: Give geometric representation of 5x + 7 = 0 as an equation

(i) in one variable (or on a number line)

(ii) in two variable (or on Cartesian plane)

Solution: (i) 5x + 7 = 0

⇒ 5x = –7

⇒ x = –7/5

= – 1.4

Equations-Of-Lines-Parallel-To-The-X-Axis-And-Y-Axis-Example-2

(ii) 5x + 0.y = –7

x	-7/5	-7/5	-7/5	-7/5
y	0	1	2	3

Equations-Of-Lines-Parallel-To-The-X-Axis-And-Y-Axis-Example-2-1

Scale : on both axis 10 lines or 1 box = 1 cm

Note:

If constant term ‘c’ is zero in equation

ax + by + c = 0 then line will pass through origin (always)