Linear Equations

A linear equation is an equation for a straight line.

Examples

These are all linear equations:

y = 3x + 2

y = 5x + 7

y = 4x − 3

Different Forms

There are many ways of writing linear equations. They usually have constants (like “3” or “c”) and must have simple variables (like “x” or “y”).

Examples

These are linear equations

y = 2x − 5

Y/2 − 3 = 2(x + 4)

2y + 3x − 4 = 0

x = 5

y =7

The variables (like “x” or “y”) in Linear Equations do NOT have:

Exponents (like the 2 in x2)

Square roots, cube roots, etc

Examples

These are NOT linear equations:

Y3 − 5 = 0

√x − y = 7

X5/3 = 125

Slope-Intercept Form

The most common form is the slope-intercept equation of a straight line:

y = mx + b

Where:

m = slope or gradient

b = y intercept

Example

y = x

Linear Equation Slope-Intercept Form

From the illustration above, we got

Slope: m = 1

Intercept: b = 0

Point-Slope Form

Another common one is the Point-Slope Form of the equation of a straight line:

Linear Equation Point-Slope Form

y − y1 = m(x − x1)

Example

y − 7 = 2(x − 4)

It is in the form y − y1 = m(x − x1) where:

y1 = 7

m = 2

x1 = 4

General Form

There is General Form of the equation of a straight line:

Ax + By + C = 0

(A and B cannot both be 0)

Example

2x − 3y + 4 = 0

It is in the form Ax + By + C = 0 where:

A = 2

B = −3

C = 4

Learn More

Solving Systems of Linear Equations Using Matrices

Lines of Symmetry of Plane Shapes

General Form of Equation of a Line

Parallel Lines

Algebra Index

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