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Finding the equation of a line

Q:  What is the equation of the line containing the points (3,5) & (6,-2)?

A:  The best place to start on this question (or on any line question in my opinion) is on the slope.

Find the slope, which we like to call “m”!  What is the slope equation?

m = (y2 – y1) / (x2 – x1)

You might also hear the slope described in words as “rise over run” or “the change in y divided by the change in x”.  The slope is basically how much you go up (or down) divided by how much you go over (left or right).

So, our points are: (3,5) & (6,-2).  Plug this into our slope equation:

m = (-2 – 5) / (6 – 3) = -7 / 3

So, we now know our slope is -7/3.

The equation of a line in slope-intercept form (which is my personal favorite) is y = mx + b.

m is the slope, b is the y-intercept

So, now  sincewe know our slope is -7/3, we can plug this in to the general equation:

y = mx + b

y = -7/3 x + b

Now, all we need to do is solve for b, then we have the whole equation!  Pick any point out of our two points to plug in.  I will pick the point (3, 5) [we know that x = 3 and y = 5, so plug those in]:

y = -7/3 x + b

5 = -7/3 * 3 + b

5 = -21/3 + b

5 = -7 + b

12 = b

Therefore, our equation is

y = -7/3 x + 12

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