What is the equation of the line perpendicular to -2x+3y=9 through (-1,-3) in standard form?

Explanation:

Anything perpendicular to Ax+By = C is of the form Bx-Ay = D

Note the swap of A and B, and how the plus sign changed to a minus sign.

In the case of -2x+3y = 9, we see that A = -2, B = 3, and C = 9.

So Bx-Ay = D updates to 3x-(-2)y = D which simplifies to 3x+2y = D

To find the value of D, plug in the given point (x,y) = (-1,-3) and simplify

3x+2y = D

D = 3x+2y

D = 3(-1) + 2(-3) ... plug in x = -1, plug in y = -3

D = -3 - 6

D = -9

Now we can say  3x+2y = D turns into  3x+2y = -9

Therefore, the line that is perpendicular to -2x+3y = 9 and it goes through (-1,-3) is 3x+2y = -9