Answer:
[tex]y=-\frac{1}{3}x+4[/tex]
Step-by-step explanation:
step 1
Find the slope of the perpendicular line
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal
(the product of their slopes is equal to -1)
In this problem
we have
[tex]y=3x+1[/tex]
The equation of the given line is [tex]m=3[/tex]
so
the slope of the perpendicular line to the given line is
[tex]m=-\frac{1}{3}[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{3}[/tex]
[tex](x1,y1)=(6,2)[/tex]
substitute
[tex]y-2=-\frac{1}{3}(x-6)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
Distribute right side
[tex]y-2=-\frac{1}{3}x+2[/tex]
[tex]y=-\frac{1}{3}x+2+2[/tex]
[tex]y=-\frac{1}{3}x+4[/tex]
