Question

Draw the graphs of linear equations $y=x$ and $y=-x$ on the same Cartesian plane. What do you observe?

Answer 1

Solution:

This is the equations of degree one and having two variables are known as linear equations in two variables. It is of the form, $ax+by+c=0$, where$a,b\&c$ are real numbers, and $a,b\ne 0$

Equations of the form $ax+by+c=0$; where a and b are real numbers, and $a,b\ne 0$, is also linear equations in two variables.

For a linear equation in two variables,

• Every point on the line will be a solution to the equation.
• Every solution of the equation will be a point on the line.

Hence, every linear equation in two variables can be represented geometrically as a straight line in a coordinate plane. Points on the line are the solution of the equation. These equations with degree one are called linear equations. This representation of a linear equation is known as graphing of linear equations in two variables.

According to the given details

$y=x$——– (i)

Values of x and y satisfying the equation are tabulated below

$x$	$-1$	$0$	$1$
$y$	$-1$	$0$	$1$

$y=-x$——- (ii)

Values of x and y satisfying the equation are tabulated below

$x$	$-1$	$0$	$1$
$y$	$1$	$0$	$-1$

On plotting the graph using the points from the above table we get

Hence, from the above graph, we can see that the two lines $y=x$and $y=-x$ intersect each other at $O(0,0).$