Okay, firstly, the standard form is:

Ax + By = C

Where A, B, and C are numbers.

Now, lets do it in point slope first. So you know that the line must be perpendicular, so the slope for the perpendicular line is:

m = -1/3

Now, use the point-slope formula first.

y + 8 = -1/3(x – 3)

Okay. Distribute.

y + 8 = -1/3x + 1

Now get 8 on the other side.

y = -1/3x – 7

Since you want the standard form, get -1/3x on the other side.

1/3x + y = -7

Now, I don’t know about you, but I don’t like fractions there. Multiply everything by 3 to get rid of it:

x + 3y = -21

That’s it.

To find the line perpendicular you need the opposite and negative of the slope you are given so m=3 would turn into m=(-1/3).

Next you would use point-slope form to solve for the new y-intercept. y-y1=m(x-x1)

So you plug in your given y1,x1, and the new m you found giving you… y-(-8)=(-1/3)(x-3)

Then you just move numbers around to get back to point-slope form. y=(-1/3)x-7

Since its a perpendicular line you know it is the opposite of 3. therefore, m(the slope) is -3. now we need to find the y-intercept(b). So, just substitute the values of the ordered pair.

(-8)=-3(3)+b

-8=-9+b

-8+9=-9+9+b

1=b

So, just put those back into the equation…

y=-3x+1

Does that help? 🙂

(y-y’)=m(x-x’)

(y+8)=-1/3(x-3)

y=-1/3x-1-8

y=-1/3x-9

I think that’s the answer.