Class 9 · Chapter 4

Linear Equations in Two Variables

Solutions of linear equations; every linear equation in two variables represents a straight line.

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Detailed theory

A linear equation in two variables

x, y

is any equation that can be written as

ax + by + c = 0

, where

a, b, c

are real and

a, b

are not both zero. Every such equation has infinitely many solutions and its graph is a straight line.

Key concepts & formulas

A linear equation in two variables has infinitely many solutions.

Graph of a linear equation is a straight line.

(x_0, y_0)

is a solution if it satisfies the equation.

y = mx + c

m

is slope,

c

y

-intercept.

Intercept form:

x/a + y/b = 1

y = k

: horizontal line;

x = k

: vertical line.