The straight line $2x - 3y + 17 = 0$ is perpendicular to the line passing through the points $(7, 17)$ and $(15, \beta)$. Then,$\beta$ equals:

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2,3)$.

The polar equation $\cos \theta + 7 \sin \theta = \frac{1}{r}$ represents a

Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $x$-intercept is $4$.

Find the equation of a straight line that makes an intercept of $3$ units on the negative direction of the $y$-axis and is inclined at an angle of ${\tan ^{ - 1}}\left( {\frac{3}{5}} \right)$ with the $x$-axis.

The slope of the line passing through the origin,which makes an angle of $30^{\circ}$ with the positive direction of the $Y$-axis measured anticlockwise,is