# How do you write the equation of the line parallel to 4x-6y=-1 with y intercept -5 in general form?

Aug 11, 2018

$2 x - 3 y - 15 = 0$

#### Explanation:

$\text{the equation of a line in "color(blue)"general form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y + C = 0} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where A is a positive integer and B, C are integers}$

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+c

$\text{where m is the slope and c the y-intercept}$

$\text{rearrange "4x-6y=-1" into this form}$

$y = \frac{2}{3} x + \frac{1}{6} \leftarrow \text{ with } m = \frac{2}{3}$

• " Parallel lines have equal slopes"

$\text{equation of parallel line is}$

$y = \frac{2}{3} x - 5 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{multiply all terms by 3}$

$3 y = 2 x - 15$

$2 x - 3 y - 15 = 0 \leftarrow \textcolor{red}{\text{in general form}}$