Answer
$3x+2y=0$
Work Step by Step
Parallel lines have equal slopes.
The given line has a slope of $-\frac{3}{2}$.
This means that the slope of the line parallel to it is also $-\frac{3}{2}$.
Thus, the tentative equation of the line is $y=-\frac{3}{2}x+b$.
To find the value of $b$, substitute the x and y-coordinates of $(-4, 6)$ into the tentative equation to have:
$y=-\frac{3}{2}x+b
\\6 = -\frac{3}{2}(-4)+b
\\6 = 6 + b
\\6-6=b
\\0=b$
Thus, the equation of the line parallel to the given line is $y=-\frac{3}{2}{x}$.
Convert this equation to $ax+by=c$ form to have:
$y=-\frac{3}{2}x
\\\frac{3}{2}x+y=0
\\2(\frac{3}{2}x+y)=0(2)
\\3x+2y=0$
