Question 17723
Suppose you have two points P(a,b) and Q(c,d)
Let the line passing through P and Q have a slope 'm'
Then {{{ m=(d-b)/(c-a)}}} 
or [difference in y-coordinates/difference of x-coordinates]
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Now take any one of the two points,say P(a,b)
We have the slope m
Taking slope-point form we get
<b>y-b=m(x-a)</b>
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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
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To make it clear,take an example
<b>There are two points A(1,5) B(4,7). Find the slope,equation and y-intercept.</b>
<font color=blue>A(1,5) B(4,7)</font>
slope m=(7-5)/(4-1)
<font color=blue>m=2/3</font>
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
<font color=blue>3y=2x+13</font>
To find y-intercept,x=0
3y=2(0)+13
3y=15
y=5
therefore,Y-intercept=<font color=blue>(0,5)</font>
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Hope this helps,
Prabhat