# How to I find the degrees of a line given it's slope?

## For example, a flagpole is tilted back and has a slope of -5 (with the ground being the x-axis). What is it's angle to the ground in degrees?

Jan 2, 2017

For a straight line when expressed in the slope-intercept form as

$y = m x + c$

we know that $m$ is the slope of the line which it makes with $x$-axis and $c$ is intercept on the $y$-axis.

Also that by definition $m \equiv \tan \theta$,
where $\theta$ is the angle line makes with the $x$-axis.

$\therefore \theta = {\tan}^{-} 1 m$

For the given problem $m = - 5$
This implies that the angle $\theta$ is more than ${90}^{\circ}$ and lies in the second quadrant as shown below.

$\theta = {\tan}^{-} 1 \left(- 5\right)$
Now using tables or a calculator we get
$\theta = - {78.7}^{\circ}$, rounded to one decimal place.
This angle is as measured from $- x$ axis in the opposite direction as indictaed by $- v e$ sign.

Or Angle of the flagpole$= 180 - 78.7 = {101.3}^{\circ}$ as measured normally.