Question 53499
Remeber that parallel lines have the same slope, so first find the slope of the given line by putting it into the "slope-intercept" form of the equation for a line:
{{{-3x+2y = 9}}} Add 3x to both sides of the equation.
{{{2y = 3x+9}}} Divide both sides by 2.
{{{y = (3/2)x+9/2}}} Compare this with the slope-intercept form:
{{{y = mx + b}}} and you'll see that the slope, {{{m = 3/2}}} so you can write:

{{{y = (3/2)x + b}}} Now, to find b, the y-intercept, you'll need to substitute the x- and y-coordinates of the given point (-2, 1) into this equation and solve for b.
{{{1 = (3/2)(-2)+b}}} Simplify and solve for b.
{{{1 = -3/4+b}}} Add {{{3/4}}} to both sides.
{{{7/4 = b}}} Now you can write the final equation of the line that is parallel to -3x+2y = 9 and which contains the point (-2, 1)

{{{y = (3/2)x+7/4}}}