Find the equation of the line perpendicular to the line $2x - 3y = 5$ and passing through the point $(1, -1)$.

$A$ straight line $L$ at a distance of $4$ units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60^o$ with the line $x + y = 0$. Then an equation of the line $L$ is

In the figure,a time-distance graph of a linear motion is given. Two positions of time and distance are recorded as: when $T = 0, D = 2$ and when $T = 3, D = 8$. Using the concept of slope,find the law of motion,i.e.,how distance depends upon time.

What is the normal form of the line $x + \sqrt{3}y - 4 = 0$?

Find the equation of the line passing through the point $(2, 3)$ and perpendicular to the line joining the points $(-5, 6)$ and $(-6, 5)$.

If a line $L$ passing through a point $A(2, 3)$ intersects another line $4x - 3y - 19 = 0$ at the point $B$ such that $AB = 4$,then the angle made by the line $L$ with the positive $X$-axis in the anti-clockwise direction is