# Decoding the straight line equation | Machine Learning

Algebra is generous; she often gives more than is asked of her — Jean le Rond

Before getting into Supervised learning branch of machine learning, it is imperative to get an idea about Linear algebra, followed by equation of straight line.

**Linear algebra** is a branch of mathematics which is concerned about linear equations. A linear equation is something which forms a line when drawn and it does have only length property, but no breadth in the mathematical space.

A form of linear equation is shown below:

The term *linear equation represents an equation of first degree. *We can also call the above equation as polynomial ( ‘**poly**’ — many and ‘**nomial**’ — terms) equation. When numbers are added or subtracted to the equation, they are called as terms.

As we can see in the above picture, the graph of first degree polynomial is always a straight line , the second degree takes the shape of parabola, third degree takes the shape of a curve. Advancing with quartic, quintic polynomials, the equation becomes too complex and graph take different shapes.

The main focus point in this article is to understand that **graph of any first degree polynomial is a straight line **and the straight line equation can be represented as below:

*y = mx + b*

Here:

- y = predicted value or target variable or dependent variable
- x = independent variable or input or predictor or feature
- m = slope / weight
- b = bias / intercept

Here m and b are constants, that defines a linear relationship between x and y. The relationship between x and y is visualized as straight line and hence the term linear.

# Introducing the straight line equation

When **y = x, **we get a straight line which **passes through the origin**. We can inflate **y = x **as below:

**y = 1.x Or**

**y = m.x, where m = 1**

Change in ‘y’ with respect to ‘x’ is represented by

**𝛿y/𝛿x = Slope **( symbol delta)

When the angle is 45 degrees ( Fig 1 ), **𝛿y/𝛿x = 1 , Since tan 𝚹 of 45 degrees = 1**

The value of **tan(45°)** can be derived exactly by theoretical approach of geometry on the basis of a geometric property. In short ‘**m**’ is the tangent of the angle that the line makes with the X axis.

Fig 2 shows different variations of straight line equations, where the value of slope changes depending the angle.

This also represents a straight line, and for all the points on the line, each **y** value is three times the corresponding x value. In all the above cases the line passes through the origin.

Now, look at the second line ( yellow line in Fig 1) where **y** is not equal to **x. **The line is represented by **y = mx +c, **where c is the intercept. When **c = 0**, the line passed through the origin. The number **c** is the point where the line cuts the **y-axis**.

The line is shifted either up or down depending on the value of **‘c’**. If the value of the intercept is positive, the line is shifted up from the origin and vice-verse.

**Conclusion**

Familiarity with linear algebra, before moving into regression algorithms, would help to write custom models in Supervised learning space. The concept of the linear regression is to find a model that represents these points in the best possible way.

Do send me your comments, thoughts to Sunil Jacob.

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