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

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.

what graph

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b