Hi! Let me help you!
- 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! :)
