How do you find the slope for 2x + 4y = 8?

2 Answers
Apr 9, 2016

Gradient is #-1/2" value corrected from "-1/4 to -1/2#

Explanation:

Given:#" "color(brown)(2x+4y=8)#

#color(blue)("Using shortcut method")#

Divide both sides by 4 so that there is no number (coefficient) in front of #y#

#2/4x+y=2" "->" corrected from "1/4x to 2/4x#

#1/2x+y=2#

But the x term is on the same side as the y term so

#color(blue)("gradient" = (-1)xx1/2=-1/2" "->" final value corrected"#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Using first principles method ")#

Subtract #color(blue)(2x)# from both sides

#" "color(brown)(2xcolor(blue)(-2x)+4y=8color(blue)(-2x))#

But #2x-2x=0# giving

#" "0+4y=-2x+8#

Divide both sides by 4

#" "4/4 xx y=-2/4 x+8/4#

But #4/4 =1" and "1xx y=y# giving

#" "x=-1/2 x+2" "->" corrected from "-1/4x" to "-1/2x#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now your equation is in standard form of

#y=mx+c# where m is the gradient

#color(blue)(=>m=-1/2)#

Apr 9, 2016

The slope (the gradient) of the function is: #-1/2#

Explanation:

If we rearrange the function to what is referred to as Gradient Form we can determine the slope (the gradient) of the function.

Gradient form can be defined as:

#y=mx+c#

Where #m# is the gradient (the slope of the line)
and #c# is the constant term of the function (effectively the y- intercept)

Therefore, if we rearrange the function you have given into Gradient Form :
#2x+4y=8#
#4y=-2x+8#
#y=-2/4x+2#
#y=-1/2x+2#
Therefore, when rearranged into Gradient Form we can see that the coefficient of #m# is #-1/2#, therefore the gradient (slope) of the function is: #-1/2#