Notes On Graphical Representation of Linear Equations in Two Variables - ICSE Class 7 Maths

An  in the form of where a, b and c are real numbers and a and b are not both zero is called a linear equation in two variables x and y.
A linear equation in two variables has infinitely many solutions.
The solutions of a linear equation can be obtained by substituting different values for x in the equation to find the corresponding values of y.
The values of x and y are represented as an order pair.
To plot the graph of this equation, we’ll first find its solutions algebraically and then plot the points on the graph.
Any linear equation of the form represents a straight line on the graph.
Every point that satisfies the linear equation lies on the line.
Every point that lies on the line is a solution of the linear equation.
A point that does not lie on the line is not solution of the linear equation.
The equation of X axis is
Any line parallel to x-axis is of the form y=k
The equation of y-axis is
Any line  parallel to y-axis is of the form x=k

Equation. Linear equation, Linear equation in one variable, solution of the linear equation, straight line, general form of a straight line, straight line equation

ax+by+c=0

y=0
x=0
y=k
x=k

Summary

An  in the form of where a, b and c are real numbers and a and b are not both zero is called a linear equation in two variables x and y.
A linear equation in two variables has infinitely many solutions.
The solutions of a linear equation can be obtained by substituting different values for x in the equation to find the corresponding values of y.
The values of x and y are represented as an order pair.
To plot the graph of this equation, we’ll first find its solutions algebraically and then plot the points on the graph.
Any linear equation of the form represents a straight line on the graph.
Every point that satisfies the linear equation lies on the line.
Every point that lies on the line is a solution of the linear equation.
A point that does not lie on the line is not solution of the linear equation.
The equation of X axis is
Any line parallel to x-axis is of the form y=k
The equation of y-axis is
Any line  parallel to y-axis is of the form x=k

Equation. Linear equation, Linear equation in one variable, solution of the linear equation, straight line, general form of a straight line, straight line equation

ax+by+c=0

y=0
x=0
y=k
x=k