ANSWER:
[tex]y=\frac{2}{3}x-1\:[/tex]STEP-BY-STEP EXPLANATION:
The equation in its slope-intercept form is as follows:
[tex]\begin{gathered} y=mx+b \\ \\ \text{ where m is the slope and b is y-intercept} \end{gathered}[/tex]We can calculate the slope since we know the slope of a perpendicular line, when the slopes are perpendicular the product of the slopes is equal to -1, therefore:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ \\ -\frac{3}{2}\cdot m_2=-1 \\ \\ m_2=\frac{2}{3} \end{gathered}[/tex]Now, we calculate the y-intercept with the slope and the point (3, 1), like this:
[tex]\begin{gathered} 1=\frac{2}{3}\cdot3+b \\ \\ 1=2+b \\ \\ b=-2+1 \\ \\ b=-1 \end{gathered}[/tex]So the equation would be:
[tex]y=\frac{2}{3}x-1\:[/tex]