For this case, we have that by definition, if two lines are perpendicular, it follows that:
[tex]m_ {1} * m_ {2} = - 1[/tex]
If we have the line: [tex]y = - \frac {3} {2} x + 4[/tex]
With slope [tex]m_ {1} = - \frac {3} {2}[/tex]
A line perpendicular to this would have slope:
[tex]m_ {2} = \frac {-1} {- \frac {3} {2}}\\m_ {2} = \frac {2} {3}[/tex]
Thus, the equation of this line is given by:
[tex]y = \frac {2} {3} x + b[/tex]
Substituting the point[tex](x, y) = (3,9)[/tex]we find the cut point "b":
[tex]9 = \frac {2} {3} 3 + b\\9 = 2 + b\\b = 9-2\\b = 7[/tex]
Thus, the equation is:
[tex]y = \frac {2} {3} x + 7\\y- \frac {2} {3} x = 7[/tex]
Multiplying by "3" on both sides of the equation:
[tex]3y-2x = 21[/tex]
Answer:
Option B
