Short answer y = x + 1
Remark
This looks like mighty fine work. I'll just do it and see if it is correct. You don't have to offer quite so many points.
Givens
Two point
(1,2) and (3,4)
Formula
slope = (y2 - y1) / (x2 - x1)
Step One
Find the slope
y2 = 4
y1 = 2
x2 = 3
x1 = 1
m = (4 - 2) / (3 - 1) = 2 / 2 = 1
Step two
Find the y intercept.
So far what we have is
y = 1x + b
y = x + b
Use (1,2) to find b
2 = 1 + b Subtract 1 from both sides.
2 -1 = b
b = 1
Equation
y = x + 1 <<<< Answer
Check
We should check to see if (3,4) will give the same result
x = 3
b = 4
4 = 3 + b Subtract 3 from both sides
4 - 3 = b
b = 1 and it does.