# How do you find the slope of a line parallel to -3y-5y=6?

Mar 29, 2017

See the solution below:

Assuming the equation is NOT $- 3 \textcolor{red}{x} - 5 y = 6$

#### Explanation:

We can rewrite this as:

$\left(- 3 - 5\right) y = 6$

$- 8 y = 6$

$\frac{- 8 y}{\textcolor{red}{- 8}} = \frac{6}{\textcolor{red}{- 8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 8}}} y}{\cancel{\textcolor{red}{- 8}}} = - \frac{6}{8}$

$y = - \frac{6}{8}$

$y = \textcolor{red}{a}$ where $\textcolor{red}{a}$ is any number is a horizontal line. A horizontal like has slope $m = 0$. Therefore any line parallel to $y = - \frac{6}{8}$ will by definition have the same slope of $m = 0$

If the problem IS for equation $- 3 x - 5 y = 6$ we can multiply each side of the equation to put this into Standard Form. The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

$- 1 \left(- 3 x - 5 y\right) = - 1 \cdot 6$

$\left(- 1 \cdot - 3 x\right) + \left(- 1 \cdot - 5 y\right) = - 6$

$\textcolor{red}{3} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{- 6}$

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Therefore, substituting the values from the equation gives a slope of:

$m = - \frac{\textcolor{red}{3}}{\textcolor{b l u e}{5}}$

Because parallel lines have the same slope, any line parallel to this line will have a slope of $m = - \frac{3}{5}$