For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
By definition, if two lines are parallel then their slopes are equal.
We have the following equation of the line:
[tex]3x-2y = 8[/tex]
We manipulate algebraically:
[tex]-2y = -3x + 8\\y = \frac {3} {2} x-4[/tex]
Thus, a parallel line will have an equation of the form:
[tex]y = \frac {3} {2} x + b[/tex]
Answer:
[tex]y = \frac {3} {2} x + b[/tex]
