Find the equation of the line which intersects the $x$-axis at a distance of $3$ units to the left of the origin with a slope of $-2$.

The intercept form of the equation of the straight line passing through the point $(4, -3)$ and perpendicular to the line passing through the points $(1, 1)$ and $(2, 3)$ is

The equation of the line parallel to $x/a + y/b = 1$ and passing through $(a, b)$ is .....

If a straight line is at a distance of $10$ units from the origin and the perpendicular drawn from the origin to it makes an angle of $\frac{\pi}{4}$ with the negative $X$-axis in the negative direction,then the equation of that line is:

The number of integral values of $m$ such that the abscissa of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer,is

The points $(1, 3)$ and $(5, 1)$ are the opposite vertices of a rectangle. The other two vertices lie on the line $y = 2x + c$. Then the value of $c$ is: