For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope
b: It is the cut point with the y axis
By definition, if two lines are parallel then their slopes are equal.
We have the following equation:
[tex]3 (y + 2) = 4x\\3y + 6 = 4x\\3y = 4x-6\\y = \frac {4} {3} x-2[/tex]
Thus, the slope is [tex]\frac {4} {3}.[/tex]
From option D we have:
[tex]-4x + 3y = 9\\3y = 4x + 9\\y = \frac {4} {3} x + 3[/tex]
Thus, the correct option is option D.
Answer:
Option D
