From the statement we have two lines, one red and the other green, which have the following properties:
A) the lines are perpendicular,
B) the green line has a slope:
[tex]m_g=-\frac{2}{3}[/tex]Because the lines are perpendicular, their slopes satisfy the following equation:
[tex]m_g\cdot m_r=-1_{}[/tex]Replacing the equation from (B) we find that:
[tex]\begin{gathered} m_r\cdot(-\frac{2}{3})=-1 \\ m_r=\frac{3}{2} \end{gathered}[/tex]Answer
The answer is option C. 3/2