Question 392234: How do I write an equation pASSING THROUGH TWO GIVEN POINTS IN SLOPE-INTERCEPT FORM?
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
I.Use the point-slope formula,  to find slope
II. then use Using the standard slope-intercept form for an equation of a line
y = mx + b where m is the slope and b the y-intercept to start the process
by substituting slope value found for m
III. use on the the ordered pairs to solve for b
IV. substitute that value found for b in the equation
For ex: Points (1,1)(5,6) m = 5/4
y = (5/4)x + b
1 = (5/4) + b
(-1/4) = b therefore: y = (4/5)x -1/4
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! example:
Find the equation of the line that passes through the points (–2, 4) and (1, 2).
Well, if I have two points on a straight line, I can always find the slope; that's what the slope formula is for.
Now I have the slope and two points. I know I can find the equation (by
solving first for " ") if I have a point and the slope. So I need to pick
one of the points (it doesn't matter which one), and use it to solve for .
Using the point (–2, 4), I get:
...so
On the other hand, if I use the point (1, 2), I get:
So it   which point I choose. Either way, the answer is the same:
As you can see, once you have the slope, it doesn't matter which point you use in order to find the line equation. The answer will work out the same either way.
in general, we have
the points (x1, y1) and (x2, y2)
slope 
............
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