To find the slope \( m \) of the angle bisector of the lines \( y = 3x \) and \( y = 2x \), we can use the formula for the slope of the angle bisector between two lines given their slopes \( m_1 \) and \( m_2 \):

Given the lines \( y = m_1 x \) and \( y = m_2 x \), the slope \( m \) of the angle bisector is given by:

\[

m = \frac{m_1 + m_2}{1 + m_1 m_2}

\]

Here, \( m_1 = 3 \) and \( m_2 = 2 \). Plugging these values into the formula, we get:

\[

m = \frac{3 + 2}{1 + 3 \cdot 2} = \frac{5}{1 + 6} = \frac{5}{7}

\]

Thus, the slope \( m \) of the angle bisector is \( \frac{5}{7} \).