Question

how do you find the slope when given an equation
?

Answer 1

If it is the equation of a straight line, put it in the form
y = m x + b
(slope intercept form)
m is the slope. The line goes up m units when you move right one unit. (if m is negative of course the line goes down one unit when you go right one unit)
If it is not a straight line, the slope of the tangent to a curve at a point is found by differentiating the function. That is calculus.

Answer 2

then how do you find the slope when only given (x,y) (x,y)

Answer 3

that is not an equation but two points.
I will call them (X1, Y1) and (X2,Y2)
then the slope is
(Y2-Y1) / (X2-X1)
that is how far you went up over how far you went right

Answer 4

i guess

Answer 5

By the way, you can find the equation for the line directly from that.
(Y2-Y1) / (X2-X1) = (y - Y1)/(x-X1)
because the slope to any point (x,y) on the line will be the same as that original slope from the two known points.