equations of parallel and perpendicular lines

Question

write the equation of a line that is perpendicular to y=7/5x +6 and that passes through the point (2,-6)

Answer 1

Given a line already, the perpendicular line's slope can be found from the fact the multiplication of the two lines' slopes must equal -1.

m₁*m₂ = -1 --> m₁ = 7/5, so m₂ = -5/7

To have the second line go through the point (2,-6). we need to solve for b

y = m₂x + b

-6 = -5/7(2) + b

b = -6 + 10/7 = -32/7

the perpendicular line which goes through the requested point is...

y = -5x/7 - 32/7 = -(5x + 32)/7