Respuesta :

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! :)

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