Given:

The line is \[\mathbf{3x}\text{ }\text{ }\mathbf{-4y}\text{ }+\text{ }\mathbf{2}\text{ }=\text{ }\mathbf{0}\]

In this way, \[\mathbf{y}\text{ }=\text{ }\mathbf{3x}/\mathbf{4}\text{ }+\text{ }\mathbf{2}/\mathbf{4}\]

\[=\text{ }\mathbf{3x}/\mathbf{4}\text{ }+\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]

Which is of the structure\[\mathbf{y}\text{ }=\text{ }\mathbf{mx}\text{ }+\text{ }\mathbf{c}\] , where m is the slant of the given line.

The incline of the given line is \[\mathbf{3}/\mathbf{4}\]

We realize that equal line have same slant.

∴ Slope of other line \[=\text{ }\mathbf{m}\text{ }=\text{ }\mathbf{3}/\mathbf{4}\]

Condition of line having slant m and going through (x1, y1) is given by

\[\mathbf{y}\text{ }\text{ }\mathbf{-y1}\text{ }=\text{ }\mathbf{m}\text{ }\left( \mathbf{x}\text{ }\text{ }\mathbf{x1} \right)\]

∴ Equation of line having slant 3/4 and going through (- 2, 3) is

\[\mathbf{y}\text{ }\text{ }\mathbf{-3}\text{ }=\text{ }{\scriptscriptstyle 3\!/\!{ }_4}\text{ }\left( \mathbf{x-}\text{ }\text{ }\left( -\text{ }\mathbf{2} \right) \right)\]

\[\mathbf{4y-}\text{ }\text{ }\mathbf{3}\text{ }\times \text{ }\mathbf{4}\text{ }=\text{ }\mathbf{3x}\text{ }+\text{ }\mathbf{3}\text{ }\times \text{ }\mathbf{2}\]

\[\mathbf{3x-}\text{ }\text{ }\mathbf{4y}\text{ }=\text{ }\mathbf{18}\]

∴ The condition is \[\mathbf{3x-}\text{ }\text{ }\mathbf{4y}\text{ }=\text{ }\mathbf{18}\]