Question

What is the equation of the line perpendicular to 2x – 3y = 13 that passes through the point (–6, 5)?

Answer 1

slope of given line is -a/b = 2/3

for perpendicular line m1*m2 = -1 hence slope of perpendicular line is -3/2

now y = m*x +c i.e. line equation

and put (-6,5) in this line

so answer is 3*x + 2*y = 14

Answer 2

2x – 3y = 13 => – 3y = 13 - 2x => – y = (13 - 2x) /3 => -y = (13/3) – (2x/3) => y = (2\3)x – (13/3). Slope is 2/3, if the point (–6, 5) has slope 2/3. 5 = (2\3) (-6) – B => 5 – 12\3 = B.

The new line equation is y = (2\3) x – (5 – 12\3) => y = (2/3) x – (15-12 \ 3) => Y = 2/3 X – (1) => 3*x + 2*y = 14