How to find the equation of a line given two points?

I'll assume you want to put the line in slope-intercept form y=mx+b. You need to find the slope m and use point slope form, which is 

You can choose y1 and x1 to be the points from the points of one of your coordinates.

Let's say you have points (1,2) and (2,4). The slope is change in y over change in x, or (y2-y1) / (x2-x1) 
m = (4-2) / (2-1) = 2/1 = 2

Choose one of the coordinates Let's do (1,2).You plug the numbers as well as the slope m into the point-slope form equation:
y - y1 = m(x - x1)
y - 2 = 2(x - 1)
y - 2 = 2x -2
y = 2x

If you don't like point slope form, then after finding the slope you can substitute it back into y=mx+b
(1,2) (2,4) and you found slope m to be 2.

You still pick one of the coordinates. But then you have to find the value of b (the y-intercept) and plug it back in for the final equation. Let's do (1,2).
y = mx + b
2 = 2(1) + b
2 = 2 + b
0 = b

So now substitute b=0, m=2 into y=mx+b
y = (2)x + 0
y = 2x