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

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

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Answer 1 · 2016-04-09T10:51:19

Gradient is $- \frac{1}{2} value corrected from - \frac{1}{4} \to - \frac{1}{2}$ $-1/2" value corrected from "-1/4 to -1/2$

Explanation:

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

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

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

$\frac{2}{4} x + y = 2 \to corrected from \frac{1}{4} x \to \frac{2}{4} x$ $2/4x+y=2" "->" corrected from "1/4x to 2/4x$

$\frac{1}{2} x + y = 2$ $1/2x+y=2$

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

$gradient = (- 1) \times \frac{1}{2} = - \frac{1}{2} \to final value corrected$ $color(blue)("gradient" = (-1)xx1/2=-1/2" "->" final value corrected"$

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

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

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

But $2 x - 2 x = 0$ $2x-2x=0$ giving

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

Divide both sides by 4

$\frac{4}{4} \times y = - \frac{2}{4} x + \frac{8}{4}$ $" "4/4 xx y=-2/4 x+8/4$

But $\frac{4}{4} = 1 and 1 \times y = y$ $4/4 =1" and "1xx y=y$ giving

$x = - \frac{1}{2} x + 2 \to corrected from - \frac{1}{4} x to - \frac{1}{2} x$ $" "x=-1/2 x+2" "->" corrected from "-1/4x" to "-1/2x$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now your equation is in standard form of

$y = m x + c$ $y=mx+c$ where m is the gradient

$\Rightarrow m = - \frac{1}{2}$ $color(blue)(=>m=-1/2)$

Answer 2 · 2016-04-09T10:59:54

The slope (the gradient) of the function is: $- \frac{1}{2}$ $-1/2$

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:

$y = m x + c$ $y=mx+c$

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

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

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

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