How do i write a slope intercept form of an equation of a line through given points ?

First you need the slope, which is easily attainable by the change of x over the change of y

ex. with coordinates (x,y)(X,Y)

m=slope
m=
   =
   = 

Then you will have every thing except the y intercept
 (represented by b)

Using the slope-intercept form 
and x and y being represented by the x, y values of a co-ordinate

y=mx+b
We can derive b

b= y-mx

Then when we have both m and b
Insert them into the form

ex. if m=-4, b=6

y=-4x+6

Taa daa!
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