[tex]\huge\boxed{\boxed{\boxed{\bf{Hi\:there!}}}}[/tex]
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, change its sign, and flop it over.
Here, we have 1/4.
First, we change its sign:
-1/4
Now, we flop it over:
-4
So the slope of the line perpendicular to the given line is -4.
Now, we are given the slope of the line and a point that the line passes through.
We can use the Point-Slope formula:
[tex]\huge\sf{y-y1=m(x-x1)[/tex]
[tex]\huge\sf{y-9=1/4(x-6)[/tex]
[tex]\huge\sf{y-9=1/4x-1.5[/tex]
[tex]\sf{y=1/4x-1.5+9\\[/tex]
[tex]\sf{y=1/4x+10.5[/tex]
[tex]\huge\boxed{Hope\:it\:helps!}[/tex]
[tex]\huge\bold{\underline{Good\:luck!}}[/tex]
[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]
