Perpendicular lines

Question

Find the equation of the line, in Ax+By=C form, that contains the point (2,1) and is perpendicular to the following line.

y=4/5x+3

Show work

Answer 1

The product of slopes of perpendicular lines is -1, so

m = -1/(4/5) = -5/4

y = (-5/4)x + b

1 = (-5/4)(2) + b

b = 7/2

y = (-5/4)x + 7/2

Multiply both sides by 4 to get integer coefficients.

4y = -5x + 14

5x + 4y = 14