Help help math math math

Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, flop it over, and change its sign.
In this case, we have a line with a slope of
[tex]\displaystyle-\frac{1}{3}[/tex]
Flop it over:
[tex]\rm{-3}[/tex]
Change its sign:
3
Thus, the slope of the line perpendicular to the given line is 3.
Now, what is its equation?
Since we know the slope and a point that the line intersects, we can write the line's equation in Point-Slope Form:
y-y1=m(x-x1)
Where y1 is the y-coordinate of the point, m is the slope, and x1 is the x-coordinate.
In this case, y1=2, m=3, and x1=4.
Plug in the values:
y-2=3(x-4)
y-2=3x-12
y=3x-12+2
y=3x-10

Answer:

y=3x-10

Hope you find it helpful.

~Nature~

Enjoy your day! :)