Question

What's the equation of the line containing the given point and perpendicular to the given line.
(5,-3);6x+5y=7
Also (4,5);6x+y=4. In the forms of y=mx+b
Thank you for your help.

Answer 1

Given: point and line.
Point: (P, Q)
Line: Ax + By = C

Since a line perpendicular to the given line will have a gradient of (B/A), and since the equation of a line with that gradient passing through the given point is:
(y-Q)=(B/A)(x-P)

Just rearrange to required format:
y = (B/A)x + (Q - BP/A)