Question

Alright, one more question.

Write the standard form of the equation of the line perpendicular to the graph of the equation
3x+2y=6 through the point (1,3).

Answer 1

@jim_thompson5910 Could you help me with one last question?

Answer 2

We're given 3x+2y=6

To find the perpendicular equation, we simply swap the '3' and '2'. Then we make the y coefficient have an opposite sign

So we'll have
2x-3y = C
where C is some constant

Answer 3

plug in the given point (1,3) to get

2x-3y = C
2*(1) - 3*(3) = C
C = ???

Answer 4

Why do we swap 3 and 2 and make y negative? Is it because we're looking for the perpendicular equation?

Answer 5

Why do we swap 3 and 2 and make y negative? Is it because we're looking for the perpendicular equation?

Answer 6

Well it's a shortcut I'm using. Did you want to do this the long way?

Answer 7

The rule I used is if you had Ax+By = C, then the perpendicular equation would be Bx-Ay = D

Answer 8

Well no... Shortcuts are greatly appreciated.. But I just want to make sure I'm completely understanding what I'm doing, for future reference. :)

Answer 9

Recall that if you had a slope of say 5/7, then the perpendicular slope is -7/5

you flip the fraction and you flip the sign

Answer 10

Ohhh alright

Answer 11

so A and B swapping and one changing signs is following that same idea

Answer 12

Okay so C is -7.

Answer 13

yes, so
2x-3y = C
becomes
2x-3y = -7

Answer 14

And that's the perpendicular equation in standard form?

Answer 15

3x+2y = 6 is the original equation
2x-3y = -7 is the perpendicular equation through (1,3)

Answer 16

`And that's the perpendicular equation in standard form?`
yes

Answer 17

the long way is to get the equation into y = mx+b form, find the perpendicular slope, then determine b, then get everything back into standard form

Answer 18

Does the flip thing you did work every time?

Answer 19

yes it does

---------------------------

Ax+By = C is equation 1
Bx-Ay = D is equation 2

I claim that equation 1 and equation 2 are perpendicular. To prove this claim, I'll need the slopes first

solve Ax+By = C for y to get y = (-A/B)x + C/B
The slope here is -A/B

solve Bx-Ay = D for y to get y = (B/A)x - D/A
the slope is B/A


Multiply the two slopes -A/B and B/A and you'll get -1

Rule: if two lines have slopes that multiply to -1, then they are perpendicular lines

so that proves equation 1 and equation 2 are perpendicular lines

Answer 20

In this case,
A = 3
B = 2
C = 6
D = -7

Answer 21

Awesome! Thank you so much!!!!

Answer 22

no problem