Answer:
You mean that if we have two pairs of points, (x1, y1) and (x2, y2)
we can find the slope of the line that conects those two points as:
a = (y2 - y1)/(x2 - x1)
remember that a linear equation has the shape:
y(x) = a*x + b
Now let's prove it:
for our case we have that
y1 = a*x1 + b
y2 = a*x2 + b
we can isolate be in both equtaions and get:
b = y1 - a*x1
b = y2 - a*x2
this means that:
y1 - a*x1 = y2 - a*x2
then:
a*x2 - a*x1 = y2 - y1
a*(x2 - x1) = y2 - y1
a = (y2 - y1)/(x2 - x1)
Which is the thing we wanted to get.
