# Linear Algebra - Linear Equation

### Table of Contents

## 1 - About

A linear equation represnts a linear function that forms a straight line.

A common form of a linear equation in the two variables (two dimensions) x and y is

<math> y= mx + b </math>

where:

- m is a constant named the slope or gradient of the line
- b is a constant named the intercept. It determines the point at which the line crosses the y-axis, otherwise known as the y-intercept.

In Statistics, it's the basic of a regression

## 2 - Articles Related

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## 3 - Assumptions

Terms of linear equations cannot contain:

- products of distinct or equal variables,
- nor any power (other than 1)
- or other function of a variable, equations involving terms such as xy, x2, y1/3, and sin(x)

## 4 - Linear Equation in

### 4.1 - Vector

In linear algebra, a linear equation can be expressed as an equation stating the value of the dot-product of:

- a coefficient vector (a vector whose entries are the coefficients)
- and a vector of unknowns variables.

Therefore a linear equation (function) is an equation of the form

<math>a . x = \beta</math>

where:

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## 5 - Type

### 5.1 - Homogeneous

A linear equation a · x = 0 with zero right-hand side is a homogeneous linear equation. A system of homogeneous linear equations is called a homogeneous linear system.

## 6 - Functions

Oracle:

- Slope: REGR_SLOPE(Y,X)
- Intercept: REGR_INTERCEPT(Y,X)