# What is the slope and intercept of 9x-6y=16?

Apr 26, 2016

$s l o p e = \frac{3}{2}$
$x = \frac{16}{9}$
$y = - \frac{8}{3}$

#### Explanation:

$\text{general line equation is given as } y = \textcolor{red}{m} \cdot x + n$

$m : s l o p e$

$9 x - 6 y = 16$

$6 y = 9 x - 16$

$y = \frac{9}{6} x - \frac{16}{6}$

$y = \textcolor{red}{\frac{9}{6}} x - \frac{16}{6}$

$s l o p e = \frac{9}{6} = \frac{3}{2}$

$\text{intercepts:}$

$\text{for x intercept : y=0}$

$0 = \frac{9}{6} x - \frac{16}{6}$

$\frac{9}{6} x = \frac{16}{6}$

$x = \frac{16}{9}$

$\text{for y intercept x=0}$

$y = \frac{9}{6} \cdot 0 - \frac{16}{6}$

$y = - \frac{16}{6}$

$y = - \frac{8}{3}$