Now take any one of the two points,say P(a,b)
We have the slope m
Taking slope-point form we get
y-b=m(x-a)

Now we have the equation,to find the yintercept put x=0
y-b=m(x-a)
y-b=m(0-a)
y-b=-am

To make it clear,take an example
There are two points A(1,5) B(4,7). Find the slope,equation and y-intercept.
A(1,5) B(4,7)
slope m=(7-5)/(4-1)
m=2/3
Equation of the line taking point A:
(y-5)=m(x-1)
y-5=2/3(x-1)
3(y-5)=2(x-1)
3y-15=2x-2
3y=2x-2+15
3y=2x+13
To find y-intercept,x=0
3y=2(0)+13
3y=15
y=5
therefore,Y-intercept=(0,5)

Hope this helps,
Prabhat