# How do you find the slope and intercept of -2x+3y-6=0?

Feb 20, 2016

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

#### Explanation:

One form of the equation of a straight line is y = mx + c , where m represents the gradient (slope) of the line and c , the y-intercept.
What makes this form useful is that m and c may be extracted quite 'easily'.

Rearrange - 2x + 3y - 6 = 0 into this form.

hence: 3y = 2x + 6

divide both sides by 3 to obtain $y = \frac{2}{3} x + 2$

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

Feb 20, 2016

Slope of the given equation is $\frac{2}{3}$ and intercept on $y$ axis is 2.

#### Explanation:

$- 2 x + 3 y - 6 = 0$ can be expressed as $3 y = 2 x + 6$ or
$y = 2 \frac{x}{3} + 2$. As a linear equation in slope intercpt form $y = m x + c$ has $m$ as slope and $c$ as intercept on $y$ axis, slope of the given equation is $\frac{2}{3}$ and intercept on $y$ axis is 2.