Answer:
[tex]y=-\dfrac{3}{2}x-1[/tex]
Step-by-step explanation:
The line 2x-3y=9 can be rewritten as
[tex]y=\dfrac{2}{3}x-3.[/tex]
The slope of this line is [tex]\dfrac{2}{3}.[/tex]
If two lines are perpendicular, then their slopes satisfy condition
[tex]m_1\cdot m_2=-1.[/tex]
Thus, the slope of the needed line is
[tex]m=-\dfrac{3}{2}.[/tex]
The equation of the line passing through the point (2,-4) and perpendicular to the line 2x-3y=9 is
[tex]y+4=-\dfrac{3}{2}(x-2),\\ \\y=-\dfrac{3}{2}x-1.[/tex]
