Question

If equation 1 is perpendicular to equation 2, rearrange and find the value of m.
Equation 1: 3=9x−2y
Equation -8=mx+3y

Answer 1

What they want you to do:
#1 ..... 3=9x−2y
2y = 9x - 3
y = (9/2)x - 3 ---> slope = 9/2

#2 ..... -8=mx+3y
-mx - 8 = 3y
(-m/3)x - 8/2 = y ----> slope = -m/3
but they are perpendicular, so
-m/3 = -2/9

solve for m

Answer 2

general slope-intercept form is ... y = m x + b ... m is slope , b is y-intercept

#1 ... adding 2y and subtracting 3 ... 2y = 9x - 3
... dividing by 2 ... y = 9/2 x - 3/2

#2 ... subtracting mx and dividing by 3 ... y = -m/3 x - 8/3

perpendicular means negative-reciprocal slopes
... 3/m = 9/2 ... 9 m = 6