We have the equation of the line 18x-3y-21=0.
18x - 3y - 21 = 0
=> -3y = 21 - 18x
=> 3y = -21 + 18x
=> y = -7 + 6x
Now y = 6x - 2 is in the form where the slope is 6 and the y-intercept is -7.
The slope of the line is the tangent of the angle it makes with the x-axis.
So if the angle made is A, tan A = 6
A = arc tan 6.
A = 80.53 degrees.
Therefore the line makes an angle 80.53 degrees with the x- axis.
The given equation of the line is 18x-3y-21=0. We rewrite the equation in slope intercept form,:18x- 21 = 3y. Or 3y = 18x-21. Dividing the equation by 3, we get:
y = 6x - 7
Therefore the slope of the line with x axis is 6.
So the angle the line 18x-3y-21=0 makes with x axis is is arc tan 6 = 80.54 degree .