What is the slope of a line parallel to the line with equation 2x – 5y = 9?

Dec 18, 2016

The slope of this line is $\frac{2}{5}$ therefore by definition the slope of any parallel line is $\frac{2}{5}$

Explanation:

The slope of two parallel lines are by definition the same. So if we find the slope of the given line we will find the slope of any line parallel to the given line.

To find the slope of the given line we must convert it to slope-intercept form.

Slope intercept form is: $\textcolor{red}{y = m x + b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{red}{b}$ is the y-intercept.

We can convert the given line as follows:

$\textcolor{red}{- 2 x} + 2 x - 5 y = \textcolor{red}{- 2 x} + 9$

$0 - 5 y = - 2 x + 9$

$- 5 y = - 2 x + 9$

$\frac{- 5 y}{\textcolor{red}{- 5}} = \frac{- 2 x + 9}{\textcolor{red}{- 5}}$

$\frac{- 5}{-} 5 y = \frac{- 2 x}{-} 5 + \frac{9}{-} 5$

$y = \frac{2}{5} x - \frac{9}{5}$

So the slope of this line is $\frac{2}{5}$ therefore by definition the slope of any parallel line is $\frac{2}{5}$