Hello, looking0glass!
You are right!
You can check your own work . . .
You have: .
Is it perpendicular to ?
Solve for . . .
Their line is: .
. . Its slope is:
Your line is: .
. . Its slope is:
Since , the line are perpendicular.
Does your line pass through (-1, 3) ?
Does (-1,3) satisfy your equation?
. . . . . Yes!
Therefore, your equation is correct.