# How do you find the slope given 6x-7y=14?

Jul 12, 2016

slope $= \frac{6}{7}$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and b, the y-intercept.

The advantage to having the equation in this form is that m and b may be extracted 'easily'.

Rearranging 6x - 7y = 14 into this form will allow us to extract m.

Subtract 6x from both sides of the equation.

$\Rightarrow \cancel{6 x} - 7 y \cancel{- 6 x} = 14 - 6 x \Rightarrow - 7 y = - 6 x + 14$

divide terms on both sides by - 7

$\frac{\cancel{- 7} y}{\cancel{- 7}} = \frac{- 6}{- 7} x + \frac{14}{- 7} \Rightarrow y = \frac{6}{7} x - 2$

Thus slope $= \frac{6}{7}$