if line ax+by=-2 is perpendicular to the line 2x-6y=14 what is the value of 3a/2b

Question

it said the answer is 9/2 but I'm confused on how to exactly find a and b

Answer 1

Perpendicular lines have a negative reciprocal slope. Slope of 1equation is equal to the negative reciprocal of the slope of the other equation

ax+by= -2

by= -ax -2

y= -ax/b -2/b

y= -a/b slope of eq. 1

2x-6y =14

-6y = -2x +14

y= -2x/-6 + 14/-6

y= 3x -7/3

slope of this perpendicular line will be negative reciprocal

y= -1/3

setting this equal to the slope of eq.1 we can solve for 3a/2b

-a/b = -1/3

-3a = -b

a= -b/-3

a=b/3

plug this value in

eq 3a/2b

3(b/3)/2b

b/2b

=1/2 answer

Answer 2

2x-6y =14

y = x/3 - 7/3

perpendicular line has negative inverse slope = -3

ax+by =-2

by = -ax -2

y =-ax/b -2/b

y=-3x -2b

-a/b = -3

a/b = 3

a =3b

3a/2b=3(3b)/2b =9b/2b = 9/2

you can't find a and b, just their ratio