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
