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

label Algebra
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May 1st, 2015

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 y-intercept

First, let's find what m is, the slope of the line...

m=y2-y1/x2-x1

m=4/6, 2/3

m=2/3

y=2/3+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:
  • (-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.
Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=2/3x+bb 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.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points

(-3,-1) and (3,3)

is

y=2/3x+1



May 1st, 2015

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