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

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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?

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Answer 1 · 2017-01-02T18:26:27

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

$y=mx+c$

![www.math-for-all-grades.com](useruploads.socratic.org)

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 $m-=tan theta$ ,
where $theta$ is the angle line makes with the $x$ -axis.

$:. theta=tan^-1m$

For the given problem $m=-5$
This implies that the angle $theta$ is more than $90^@$ and lies in the second quadrant as shown below.
![img.sparknotes.com](useruploads.socratic.org)

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

Or Angle of the flagpole $=180-78.7=101.3^@$ as measured normally.

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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?

1 Answer

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