In order to find the slope of the perpendicular line, let's first find the slope of these two points.
We can find it using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, using the points (3, -5) and (1, 9), we have:
[tex]m=\frac{9-(-5)}{1-3}=\frac{14}{-2}=-7[/tex]So the slope of this line is -7.
In order to find a perpendicular line, the slopes of the lines need to have the following relation:
[tex]m_1=-\frac{1}{m_2}[/tex]Using m1 = -7, we have:
[tex]\begin{gathered} -7=-\frac{1}{m_2} \\ m_2=-\frac{1}{-7}=\frac{1}{7} \end{gathered}[/tex]So the slope of the perpendicular line is 1/7.
