# How do you find the slope and intercept of 2x +3y = 12?

Mar 21, 2018

slope $m = - \frac{2}{3} \mathmr{and} Y$ -intercept $= 4$

#### Explanation:

If the equation of the line is $a x + b y + c = 0$,then

$s l o p e : m = - \frac{a}{b} \mathmr{and} Y$-intercept $= - \frac{c}{b} .$

we have,

$2 x + 3 y = 12$

$\implies 2 x + 3 y - 12 = 0 \implies a = 2 , b = 3 , c = - 12$

So, slope $m = - \frac{2}{3} \mathmr{and} Y$ -intercept #=-(-12)/3=12/3=

OR
$2 x + 3 y = 12 \implies 3 y = - 2 x + 12 \implies y = \left(- \frac{2}{3}\right) x + \frac{12}{3}$
$y = \left(- \frac{2}{3}\right) x + 4$

Comparing with $y = m x + c ,$

where m is the slope and c is the y-intercept

we get $m = - \frac{2}{3} \mathmr{and} c = 4$