Two straight lines u = 0 and v = 0 pass through the origin and the angle between them is ${\tan }^{-1}(7/9)$.If the ratio of the slope of v = 0 and   u = 0 is 9/2, then their equations are 

Let the slope of u= 0 be m. Then slope of v=0 is 9m/2. Therefore,

$\begin{array}{rl} & \frac{7}{9}=\left|\frac{\mathrm{m}-\frac{9\mathrm{m}}{2}}{1+\mathrm{m}\times \frac{9\mathrm{m}}{2}}\right|=\left|\frac{-7\mathrm{m}}{2+9{\mathrm{m}}^2}\right|\\ \mathrm{or} & 9{\mathrm{m}}^2-9\mathrm{m}+2=0\text{or}9{\mathrm{m}}^2+9\mathrm{m}+2=0\\ & \mathrm{m}=\frac{9\pm \sqrt{81-72}}{18}=\frac{9\pm 3}{18}=\frac{2}{3},\frac{1}{3}\\ \mathrm{or} & \mathrm{m}=\frac{-9\pm 3}{18}=-\frac{2}{3},-\frac{1}{3}\end{array}$

Therefore, the equations of the lines are

(i) 3y= x and 2y=3x
(ii) 3y = 2x and y= 3x
(iii) x+3y-0 and 3x+2y=0
(iv) 2x+3y=0and3x+y=0