2x + 3y = 3
Solve in the form y=mx+c (m=slope)
3y = -2x + 3
y= (-2/3) x + 3/3
y= (-2/3) x + 1
m = -2/3
Parallel lines have same slope.
use the given point,
x=3, y=-4, m= -2/3
y = mx + c
-4 = (-2/3) 3 + c
-4 = -2 + c
c = -2
Put it in y=mx+c format,
y = (-2/3) x - 2
Hence, the equation of the line that is parallel to 2x + 3y = 3 is y=(-2/3) x - 2.
