# What is the slope of 8=-12y+14x?

Jul 28, 2016

Slope is $\frac{7}{6}$

#### Explanation:

$\textcolor{b l u e}{\text{Using short cuts - part calculation}}$

We need to have a single $y$ with no coefficient. So divide everything by 12. So $14 x \to \frac{14}{12} x = \frac{7}{6} x$

As $- 12 y$ is on the right and we would need to move it to the left to get +y on its own the $+ 14 x$ is on the correct side.

So $14 x \to \frac{14}{12} x = \frac{7}{6} x$ is on the correct side and positive

So the slope is $+ \frac{7}{6}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Using first principles - full calculation}}$

$\textcolor{p u r p \le}{\text{The Short Cut method uses First Principles but}}$
$\textcolor{p u r p \le}{\text{skips steps so it is faster.}}$

You need to change this into the format of
$y = m x + c \text{ }$ where m is the slope (gradient")

Multiply both sides by $\left(- 1\right)$ making the $y$ term positive.

$- 8 = + 12 y - 14 x$

Add $14 x$ to both sides giving

$\textcolor{b r o w n}{- 8 \textcolor{b l u e}{+ 14 x} = 12 y - 14 x \textcolor{b l u e}{+ 14 x}}$

$- 8 + 14 x = 12 y + 0$

Divide both sides by $\textcolor{b l u e}{12}$

color(brown)(-8/(color(blue)(12)) +(14x)/(color(blue)(12))=12/(color(blue)(12))xxy

$\textcolor{g r e e n}{y = \frac{7}{6} x - \frac{2}{3}}$

$\textcolor{g r e e n}{\underline{\overline{| \textcolor{w h i t e}{\frac{2}{2}} m = \frac{7}{6} \textcolor{w h i t e}{\frac{2}{2}} |}}}$