Linear Equation: Definition, Formula, Graph, Standard Forms, Examples

The Linear Equation is an interesting concept in mathematics. A linear equation can represent any straight line drawn on a plane. It provides a simple way to calculate the value of unknown variables that we often need to solve in real-life scenarios.

What is a Linear Equation?

How to Identify Linear Equations?

Linear Equation Formulas

Slope-Intercept Form

• m = slope (how steep the line is)
• c = y-intercept (where the line crosses the y-axis)

Example : If the equation is y = 2x + 3y

• The slope ( m ) is 2 , meaning the line rises 2 units for every 1 unit it moves right.
• The y-intercept ( c ) is 3 , meaning the line crosses the y-axis at (0,3).

Point-Slope Form

• (x ₁ y ₁ ) is a point on the line
• m is the slope

Example :

Simplify:

Slope Formula

Example :

• (x ₁ ,y ₁ ) = (1,2)
• (x ₂ , y ₂ ) = (3, 6)

Substituting the values:

Linear Equation Standard Form

For example,

Graphical Representation of a Linear Equation

Slope-Intercept Form of Linear Equation

Point-Slope Form of Linear Equation

Solving Linear Equations

Solving Linear Equation with One Variable

Solving Linear Equation with Two Variables

• Arrange the equations in the standard form: ax + by + c = 0
• Check if adding or subtracting the equations would result in the cancellation of a variable.
• If not, multiply one or both equations by either of the coefficients of x or y so that their addition or subtraction would cancel any of the variables.
• An equation with a single variable will be obtained.
• Solve the equation for the single variable.
• Put the value of this variable in any of the given equations to get the value of another variable.

Linear Equations Solved Examples

1. Three times a number when added to 21, the result is 60. Find the number.

Solution:

2. Riya is 5 years older than Rina. If the sum of their ages is 23, find their ages.

Solution: