Find line perpendicular to 2x+3y=9 through the point (2,1)

Question

itsonlycdeee · Answer

3y = -2x + 9 
y = -2/3x + 3
perpendicular means the new line will be y = 3/2x + b. Now plug in the point (2,1) to find b & you have the new line.

anonymous · Answer

how do i plug in (2,1) @itsonlycdeee

itsonlycdeee · Answer

With (2, 1) . x = 2 & y = 1 
1 = 3/2 (2) + b . Can you solve the rest from there?

the_fizicx99 · Answer

Convert 2x+3y=9 into y = mx + b

2x+3y=9

Subtract both sides 2x

3y = -2x + 9

Divide every term by 3 to isolate y,

y = -2/3x + 3

So now you have your point slope formula, now its asking for the perpendicular so its the reciprocal, -2/3 --> 3/2

y = 3/2x + 3


Your slope or M = 3/2.
_____________________________

Now plug in the coordinates into: Y-y1 = M(x-x1)

Y - 1=3/2(x-2)

Distribute 3/2 to x and -2

y - 1 = 3/2x - 3

Add 1 to both sides,

y = 3/2x -2

So that's your new equation

anonymous · Answer

Thank you both! @itsonlycdeee @tHe_FiZiCx99

the_fizicx99 · Answer

Np, you're welcome :3

itsonlycdeee · Answer

No problem!