# ML: Simple Math

Simply put, Machine Learning is about training a machine (model) to predict output for a given input.

Let us try to understand the math behind the prediction part.

Can you predict a missing number in the pattern below?

```r
(1, 10)
(2, 20)
(3, 30)
(4, 40)
(5, ?)
```

That was quite simple. Try another one...

```r
(0, 5)
(2, 3)
(6, -1)
(4, ?)
```

This one isn't that obvious. But there's a simple way. Let us treat these as `(x,y)` co-ordinates and try to plot a graph.

![](https://cdn.hashnode.com/res/hashnode/image/upload/v1689576975911/74a74a1d-ef67-4716-a8bc-b8a7d7d71a2b.png align="center")

Now, were you able to find the missing number? Yes, it is 1 (the red dot).

Can we do it without a graph? The answer is a **linear equation**.

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named a 'linear' equation.

The linear equation is given as -

> y = mx + b

where,

m = slope ([know more](https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/introduction-to-slope))

b = y-intercept (the point at which the line intersects the Y-axis) ([know more](https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:x-intercepts-and-y-intercepts/v/introduction-to-intercepts))

Now, to find the value of `y` using the linear equation, for a given `x` we will need values of the slope `m` and the y-intercept `b`.

Consider the given points.

```r
(x, y)
(0, 5)
(2, 3)
(6, -1)
```

Fortunately, we have a point with `x = 0` so finding `b`, the y-intercept is easy.

Using the first point `(x, y) = (0, 5)` :

```r
y = m * x + b
5 = m * 0 + b
5 = 0 + b
5 = b
```

we got `b = 5`.

---

Using `b` as 5 and the second point in the table `(x, y) = (2, 3)`, let us find `m`, the slope.

```r
y = m * x + b
3 = m * 2 + 5
3 - 5 = m * 2
-2 = m * 2
-2 / 2 = m
-1 = m
```

we got `m = -1`.

---

Let us use `m = -1` and `b = 5` to find the missing number.

```r
(x, y)
(4, ?)

y = m * x + b
y = -1 * 4 + 5
y = -4 + 5
y = 1
```

We were finally able to find the missing number, 1.

---

In the next one, [ML: Simple Model](https://blog.niranjanborawake.in/ml-simple-model), we'll try to train a model to predict the value for the same example above.