# How do you find the slope and intercept for 2x-3y=12?

Mar 7, 2016

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

#### Explanation:

One form of the equation of a line is y = mx + c , where m represents the gradient (slope) and c , the y-intercept.

Rearrange 2x - 3y = 12 into this form and extract m and c.

hence : - 3y = -2x + 12

divide both sides by - 3

$\Rightarrow \frac{\cancel{- 3} y}{\cancel{- 3}} = \frac{- 2 x}{- 3} + \frac{12}{-} 3$

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

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