What is the answer to this Algebraic problem?

Question

"Find the equation of the line perpendicular to Ax+By=C through the point (2,11)"

I would really appreciate it if someone can answer this for me! I don't have a clue on how to even begin this question. Thank you in advance for any answers!

Answer 1

Since Ax + By = C, By = -Ax + C. So, y = (-A/B)x + C/B.

This line has slope -A/B.

Any line perpendicular to the line with equation Ax + By = C has slope -1 / (-A/B) = B / A.

Equation of line with slope B / A and containing the point (2,11) is:

y - 11 = (B/A)(x - 2)