# How do you find the slope and intercept of 5(x-3y)=2(x+3)?

Aug 29, 2016

Slope of the line is $\frac{1}{5}$ and intercept on $y$-axis is $- \frac{2}{5}$

#### Explanation:

The equation of a line in slope intercept form is $y = m x + c$, where $y$ is expressed in terms of $x$ and then $m$, the coefficient of $x$, is slope and $c$ the constant term is the value of intercept made by the line on $y$-axis.

In the equation $5 \left(x - 3 y\right) = 2 \left(x + 3\right)$, we simplify and write $y$ in terms of $x$.

$5 \left(x - 3 y\right) = 2 \left(x + 3\right)$

$\Leftrightarrow 5 x - 15 y = 2 x + 6$ or

$- 15 y = 2 x - 5 x + 6$ or

$- 15 y = - 3 x + 6$ or

$y = \frac{- 3}{- 15} x + \frac{6}{- 15}$ or

$y = \frac{1}{5} x - \frac{2}{5}$

Hence slope of the line is $\frac{1}{5}$ and intercept on $y$-axis is $- \frac{2}{5}$.