# How do I calculate a linear equation?

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Check the document that i attached, for more information

**Sources:**

A linear equaton colud be compaeared as weights on a a scale, you know some weghts vaue, the weights "x" none

when we have i.e:

`7x +5 = x + 17`

the symbol "equal" means tha wheights on the left and right side are equivalents.

Now You can immagine the left side as sum of a known weight `5` and seven weights of value `x`

On the right side we have a weight of value `17` an only one weight of value: `x`

First step is to separate `x` weigts and know values keeping the equivalence. To do this we have , step by step, ad or subtract same weights.

In the example, if we take an x weights both sides, we get:

`7x + 5 - x = x + 17 - x`

subtracting by like terms:

`6x + 5=17`

You can see this operation allow us to have `x` weights only on lefs side .

But we havent separate `x` from known yet

To mange this we have to deed wit another subraciono taking away

the weight `5` from both sides, this in order to manage only `x` on the left side an known weight on the rigth side.

`6x +5 -5 =17 -5`

having subtract the weight `5` from both sidethe scale is still in the balance.

So operating with similar terms we get:

`6x = 12`

At once we know, if six equal weights acting as a weight of value

`12` only singe weights `x` act as `12/6` that is `2`

So:

FIRST STEP: SEPARTING X VALUE FROM KNOW VALUE

SECOND STEP: IS DIVIDE KNOWN VALUE BY NUMBER OF `x` is on the other side of the scale.

What I under stand from your question is that regression line of the form

Y=a+bX

Y and X are two variables . a,b are constant to be determined as.

`sum_(i=1)^nY=sum_(i=1)^na+sum_(i=1)^nbX`

`sum_(i=1)^nY=na+bsum_(i=1)^nX``................(i)`

`sum_(i=1)^nXY=asum_(i=1)^nX+bsum_(i=1)^nX^2............(ii)`

solving system of equation (i) and (ii) for a,b. we can get regression line.