The equation of the line whose slope is $3$ and which cuts off an intercept of $3$ from the positive $x$-axis is

Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point where it meets the $y-$ axis.

The length of the perpendicular from the origin to a line is $7$ and the line makes an angle of $150^{\circ}$ with the positive direction of the $y$-axis. Find the equation of the line.

If the line passing through the point $(4, -3)$ and having a negative slope makes an angle of $45^{\circ}$ with the line joining the points $(1, 1)$ and $(2, 3)$,then the sum of the intercepts of that line is:

Find the equation of the line passing through $(4, 6)$ and parallel to the line $3x - 7y + 2 = 0$.

If $(a, 8)$ is a point on the line segment joining $(2, 5)$ and $(4, -1)$,then the value of $a$ is: