How to find a equation from a graph with the points already given to you?
Algebra

Tutor: None Selected  Time limit: 1 Day 
You want to find the equation for a line that passes through the two points:(3,1) and (3,3).
First of all, remember what the equation of a line is:
y = mx+bWhere: m is the slope, and
 b is the yintercept
First, let's find what m is, the slope of the line...
m=y2y1/x2x1
m=4/6, 2/3
m=2/3
y=2/3+b
Now, what about b, the yintercept?
To find b, think about what your (x,y) points mean:Because you said the line passes through each one of these two points, right?
 (3,1). When x of the line is 3, y of the line must be 1.
 (3,3). When x of the line is 3, y of the line must be 3.
Now, look at our line's equation so far: y=^{2}/_{3}x+b. b is what we want, the ^{2}/_{3} is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (3,1) and (3,3).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the
same:
 (3,1). y=mx+b or 1=^{2}/_{3} × 3+b, or solving for b: b=1(^{2}/_{3})(3). b=1.
 (3,3). y=mx+b or 3=^{2}/_{3} × 3+b, or solving for b: b=3(^{2}/_{3})(3). b=1.
The equation of the line that passes through the points (3,1) and (3,3) is y=^{2}/_{3}x+1 
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