How do you find the slope of 2x-4y=8?

2 Answers
Mar 15, 2018

m = #1/2#

Explanation:

#y=1/2x-2# put in slope-intercept form by solving for y
Slope = #1/2#

Mar 15, 2018

Slope is #+1/2#

Explanation:

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#