SOLUTION: What point-slope form equations could be produced with the points (6, 7) and (4, 3)?

Question 1159379: What point-slope form equations could be produced with the points (6, 7) and (4, 3)?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

There are two answers
y - 7 = 2(x - 6)
or
y - 3 = 2(x - 4)

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How to get those answers:

First we need the slope of the line through (6, 7) and (4, 3)

Using the slope formula, we get,
m = (y2 - y1)/(x2 - x1)
m = (3 - 7)/(4 - 6)
m = (-4)/(-2)
m = 2
The slope is 2

Let's focus solely on the point (6,7) for now
Plug m = 2 and (x1,y1) = (6,7) into the point slope formula.
y - y1 = m(x - x1)
y - 7 = 2(x - 6)
This is one point-slope form equation that goes through the two points mentioned.

We could use the second point (4,3) in place of (6,7) as the order of the points does not matter. The slope remains the same.
Let m = 2 and (x1,y1) = (4,3)

We then have
y - y1 = m(x - x1)
y - 3 = 2(x - 4)
which is the other answer

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Extra Info:

As you can see, there are multiple ways to write the equation of a line in point slope form. If we knew other points on this same line, we could use them as well. This means infinitely many points can be considered, leading to infinitely many equations. However, when you solve for y to get it into y = mx+b form (slope intercept form), then you should get one unique answer only.

Solving either y - 7 = 2(x - 6) or y - 3 = 2(x - 4) for y leads to y = 2x-5
This is in the form y = mx+b with m = 2 as the slope and b = -5 as the y intercept

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