Answer :
First, we need to find the slope of the line that passes through the points (6,-5) and (2,1).
The slope (m) of the line that passes through the points (x1, y1) and (x2, y2) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}_{}[/tex]Replacing with the points (6,-5) and (2,1), we get:
[tex]m_1=\frac{1-(-5)}{2-6}=\frac{6}{-4}=-\frac{3}{2}[/tex]Two lines are perpendicular when the multiplication of their slopes is equal to minus one. Then, the slope (m2) of a line perpendicular to one with points (6,-5) and (2,1) is:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{3}{2}\cdot m_2=-1 \\ m_2=-1\cdot-\frac{2}{3} \\ m_2=\frac{2}{3} \end{gathered}[/tex]