Question

Why do we subtract the y-values and subtract the x-values to find the slope?

Answer 1

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.