Answer:
[tex]y=\frac{-3}{2}x-4[/tex]
Step-by-step explanation:
the equation of the line perpendicular to 2x – 3y = 13
It passes through the point (–6, 5)
[tex]2x -3y = 13[/tex]
Subtract 2x from both sides
[tex]-3y =-2x+13[/tex]
Divide both sides by -3
[tex]y=\frac{2}{3}x-\frac{13}{3}[/tex]
Slope = 2/3
Slope of perpendicular lines are negative reciprocal of one another
slope of perpendicular line is [tex]\frac{-3}{2}[/tex]
Point (-6,5)
[tex]y-y1=m(x-x1)[/tex]
[tex]y-5=\frac{-3}{2}(x+6)[/tex]
[tex]y-5=\frac{-3}{2}x-9[/tex]
Add 5 on both sides
[tex]y=\frac{-3}{2}x-4[/tex]
