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
Jan 2, 2017

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

#y=mx+c#

www.math-for-all-grades.com

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

# 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.