Question

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

Answer 1

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)`

Answer 2

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`