Answer
$3x+2y=6$
Work Step by Step
Perpendicular lines have slopes that are negative reciprocals of each other.
The given line has a slope of $\frac{2}{3}$.
This means that the slope of the line perpendicular to it is $-\frac{3}{2}$.
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 $(-2, 6)$ into the tentative equation to have:
$y=-\frac{3}{2}x+b
\\6 = -\frac{3}{2} (-2)+b
\\6=3+b
\\6-3=b
\\3=b$
Thus, the equation of the line parallel to the given line is $y=-\frac{3}{2}x+3$.
Convert this equation to $ax+by=c$ form to have:
$y=-\frac{3}{2}x+3
\\\frac{3}{2}x+y=3
\\2(\frac{3}{2}x+y)=3(2)
\\3x+2y=6$
