\[\left( \mathbf{i} \right)\text{ }\mathbf{3x}\text{ }+\text{ }\mathbf{2y}\text{ }\text{ }\mathbf{-12}\text{ }=\text{ }\mathbf{0}\]

Given:

The condition is \[\mathbf{3x}\text{ }+\text{ }\mathbf{2y}\text{ }\text{ }\mathbf{-12}\text{ }=\text{ }\mathbf{0}\]

Condition of line in block structure is given by\[\mathbf{x}/\mathbf{a}\text{ }+\text{ }\mathbf{y}/\mathbf{b}\text{ }=\text{ }\mathbf{1}\] , where ‘a’ and ‘b’ are captures on x pivot and y – hub individually.

Along these lines, \[\mathbf{3x}\text{ }+\text{ }\mathbf{2y}\text{ }=\text{ }\mathbf{12}\]

presently let us partition the two sides by 12, we get

\[\mathbf{3x}/\mathbf{12}\text{ }+\text{ }\mathbf{2y}/\mathbf{12}\text{ }=\text{ }\mathbf{12}/\mathbf{12}\]

\[\mathbf{x}/\mathbf{4}\text{ }+\text{ }\mathbf{y}/\mathbf{6}\text{ }=\text{ }\mathbf{1}\]

∴ The above condition is of the structure\[\mathbf{x}/\mathbf{a}\text{ }+\text{ }\mathbf{y}/\mathbf{b}\text{ }=\text{ }\mathbf{1}\] , where \[\mathbf{a}\text{ }=\text{ }\mathbf{4},\text{ }\mathbf{b}\text{ }=\text{ }\mathbf{6}\]

Catch on x – axis is \[\mathbf{4}\]

catch on y – axis is \[\mathbf{6}\]

\[\left( \mathbf{ii} \right)\text{ }\mathbf{4x-}\text{ }\text{ }\mathbf{3y}\text{ }=\text{ }\mathbf{6}\]

Given:

The condition is \[\mathbf{4x-}\text{ }\text{ }\mathbf{3y}\text{ }=\text{ }\mathbf{6}\]

Condition of line in block structure is given by\[\mathbf{x}/\mathbf{a}\text{ }+\text{ }\mathbf{y}/\mathbf{b}\text{ }=\text{ }\mathbf{1}\] , where ‘a’ and ‘b’ are captures on x pivot and y – hub individually.

Along these lines, \[\mathbf{4x-}\text{ }\text{ }\mathbf{3y}\text{ }=\text{ }\mathbf{6}\]

Presently let us partition the two sides by 6, we get

\[\mathbf{4x}/\mathbf{6+}\text{ }\text{ }\mathbf{3y}/\mathbf{6}\text{ }=\text{ }\mathbf{6}/\mathbf{6}\]

\[\mathbf{2x}/\mathbf{3+}\text{ }\text{ }\mathbf{y}/\mathbf{2}\text{ }=\text{ }\mathbf{1}\]

\[\mathbf{x}/\left( \mathbf{3}/\mathbf{2} \right)\text{ }+\text{ }\mathbf{y}/\left( -\text{ }\mathbf{2} \right)\text{ }=\text{ }\mathbf{1}\]

∴ The above condition is of the structure\[\mathbf{x}/\mathbf{a}\text{ }+\text{ }\mathbf{y}/\mathbf{b}\text{ }=\text{ }\mathbf{1}\] , where \[\mathbf{a}\text{ }=\text{ }\mathbf{3}/\mathbf{2},\text{ }\mathbf{b}\text{ }=\text{ }-\text{ }\mathbf{2}\]

Catch on x – axis is \[\mathbf{3}/\mathbf{2}\]

Catch on y – axis is \[-\text{ }\mathbf{2}\]