For this case we must indicate a line perpendicular to:
[tex]y = \frac {2} {3} x-4[/tex]
By definition, if two lines are perpendicular, the product of their slopes is -1, that is:
[tex]m_ {1} * m_ {2} = - 1[/tex]
If we have that [tex]m_ {1} = \frac {2} {3}[/tex]then:
[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {\frac {2} {3}}\\m_ {2} = \frac {3 * -1} {2}\\m_ {2} = - \frac {3} {2}[/tex]
Thus, a line perpendicular to the given line will have a slope of[tex]- \frac {3} {2}.[/tex]
Then, the correct option is option A.
ANswer:
Option A
