Consider the standardised form of #y=mx+c# wher #m# is the gradient (slope).
We need to manipulate #2x-4y=8# into this form
With a bit of practice you may be able to some of these in your head without having to manipulate.
First of all we need to make the #y# term positive.
Multiply everything on both sides by (-1) giving:
#-2x+4y=-8#
Now we isolate (get on its own) the #4y#
Add #color(red)(2x)# to both sides. When combined with #-2x# on the left side they become 0
#color(green)(-2x+4y=-8 color(white)("ddd")->color(white)("ddd")ubrace(-2xcolor(red)(+2x))+4y=-8color(red)(+2x))#
#color(green)(color(white)("dd.dddddddddddddd")->color(white)("dddddd")0color(white)("ddd")+4y=2x-8 )#
Now we 'get rid' of the 4 from #4y#
Divide all of both sides by #color(red)(4)#
#color(green)(4y=2x-8 color(white)("ddddddd")->color(white)("ddddddddddd")4/color(red)(4)y=2/color(red)(4)x-8/color(red)(4)#
But #4/4=1 and 2/4=1/2 and 8/4=2# giving
#color(green)(color(white)("ddddddddddddddddd")->color(white)("ddddddddddddd")y=1/2x-2)#
Compare to #................................................y=mx+c#
The gradient (slope) #=m=1/2#
