If the line $y = mx + c$ passes through the points $(2, 4)$ and $(3, -5)$,then:

Find the number of integer values of $m$ such that the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is an integer.

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:

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.

The vertex $A$ of a triangle lies on the lines $x+y=1$ and $2x+3y=6$. If the orthocentre of the triangle is $O\left(\frac{3}{7}, \frac{22}{7}\right)$,then the equation of $OA$ in the normal form is

$A$ line $AB$ passes through the origin $(0, 0)$ and is perpendicular to the line $CD$ given by $3x + 4y + 6 = 0$. The equation of line $AB$ is: