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

Apr 9, 2016

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

#### Explanation:

Given:$\text{ } \textcolor{b r o w n}{2 x + 4 y = 8}$

$\textcolor{b l u e}{\text{Using shortcut method}}$

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

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

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

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"

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Using first principles method }}$

Subtract $\textcolor{b l u e}{2 x}$ from both sides

$\text{ } \textcolor{b r o w n}{2 x \textcolor{b l u e}{- 2 x} + 4 y = 8 \textcolor{b l u e}{- 2 x}}$

But $2 x - 2 x = 0$ giving

$\text{ } 0 + 4 y = - 2 x + 8$

Divide both sides by 4

$\text{ } \frac{4}{4} \times y = - \frac{2}{4} x + \frac{8}{4}$

But $\frac{4}{4} = 1 \text{ and } 1 \times y = y$ giving

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

Now your equation is in standard form of

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

$\textcolor{b l u e}{\implies m = - \frac{1}{2}}$

Apr 9, 2016

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

#### 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:

$y = m x + c$

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