Question

What is the equation of a line that is perpendicular to 2x+3y=9 and passes through the point (8,5)

Answer 1

For
ax+by=c
slope=-a/b

perpendiculare lines have slopes that multiply to -1

so

2x+3y=9
slope=-2/3
-2/3 times what=-1
what=3/2


point slope form
the equation of a line that passes through the point (x1,y1) and the slope is m is
y-y1=m(x-x1)
slope=3/2
point i (8,5)

equation is
y-5=3/2(x-8)
converted to standard form
2y-10=3x-24
-3x+2y=-14
3x-2y=14

Answer 2

2x+3y=9
3y = -2x + 9
y = -2/3x + 3
slope = -2/3 so perpendicular slope = 3/2

y - 5 =  3/2 (x - 8)
y - 5 =  3/2x -12 
y = 3/2x - 12 + 5
y = 3/2x - 7