The slope-intercept form is
[tex]y=mx+b[/tex]where m is the slope and be the y-intercept
then we need to know that the slope of a line perpendicular to another is the inverse of the slope
y=3x+2
m1=3
the inverse of this slope is
m2=-1/3
then we have slope- point form
[tex]y-y_1=m(x-x_1)[/tex]where
m=-1/3
point (1,3)=(x1,y1)
then we substitute the values
[tex]y-3=-\frac{1}{3}(x-1)[/tex]we isolate the y in order to have the equation in slope-intercept form
[tex]\begin{gathered} y=-\frac{1}{3}x+\frac{1}{3}+3 \\ y=-\frac{1}{3}x+\frac{10}{3} \end{gathered}[/tex]