In analytical geometry, there are already derived equations to find the distance of lines and points as well as the angle made between two lines. As special case is when the other line is one of the coordinate axis. Then, the formula can be simplified to
tan θ =m, where m is the slope of the equation
In the next step, we also incorporate operations of calculus. Since the slope is equal to Δy/Δx, this is equivalent to dy/dx in calculus. Therefore, you can find the slope by differentiating the equation in terms of x.
y-2x=7
y = 2x+7
dy/dx = 2 =m
So,
tan θ = 2
θ = tan⁻¹(2)
θ = 63.43°