What is the slope and y-intercept of this line 8x + 6y = 12?

May 22, 2016

slope$= - \frac{4}{3}$
y-intercept = 2

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 equation in this form is useful as m and b can be extracted 'easily'

If we rearrange 8x + 6y = 12 into this form then m and b can be found.

hence : 6y = 12 - 8x = - 8x +12

divide both sides by 6.

$\Rightarrow \frac{\cancel{6} y}{\cancel{6}} = \frac{- 8}{6} x + \frac{12}{6} \text{ and simplifying gives}$

$y = - \frac{4}{3} x + 2$

$\Rightarrow \text{slope"=-4/3" and y-intercept} = 2$