\[\boxed{\text{1163.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[y = \frac{4x + 3}{4x^{2} + 3x} = \frac{4x + 3}{x(4x + 3)} = \frac{1}{x};\ \]
\[\ \ \ x \neq 0;\ \ x \neq - \frac{3}{4}.\]
\[y = - \frac{4}{3};\]
\[- \frac{3}{4}k = - \frac{4}{3}\]
\[k = \frac{4}{3} \cdot \frac{4}{3} = \frac{16}{9}.\]
\[при\ k = \frac{16}{9}\ прямая\ y = kx\ \]
\[имеет\ с\ графиком\ ровно\ \]
\[одну\ общую\ точку.\]