Slope intercept term has only a y on the left, followed 
by an equal sign. The first term on the right is a number 
multiplied by x. The second and last term on the right is 
just a number.

 4x+y = 8

Subtract 4x from both sides

   y = 8-4x

Reverse the term on the right:

   y = -4x+8

That's it!  Now you compare that to

   y = mx+b

and you see that m=-4 and b=8

That means that the slope is -4 and the y-intercept
is the point (0,8) and that the graph of the equation
is this line: 



Notice that it passes through (0,8) and it falls 4 units
of y, for every unit of x that you go to the right.

Edwin