How do I find the angle a line makes with the x axis when given the gradient of the line?

If someone could explain how to do this it would be much appreciated.How do I find the angle a line makes with the x axis when given the gradient of the line?
Trigonometry





Given y = mx + c,


you know the gradient is m








remember that the gradient is rise / run


which is the same as opposite / hypothenuse





so the angle is tan-1 (inverse tan) the gradient.





Eg a gradient of 1


= tan-1(1)


= 45 degreesHow do I find the angle a line makes with the x axis when given the gradient of the line?
Gradiant of the line is nothing but its slope . Slope is the tangent of the angle which the line makes with the POSITIVE x-axis . So you need to fin the tan of the gradiant and that will be the angle which the line will makewith the axis of abcissa (x axis)


For instance let the line be 2x + 2y =7


Writing the expression in the form y=mx +c we get


y=-x+7/2 . Comparing it with y=mx+c , we get m=-1 , which is nothing but its slope . So , let this line make an angle w with x axis


So , tan(w) =-1 .


So w= pie-pie/4


=3pie/4 radians .