Answer
$y=-\dfrac{2}{3}x +6$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b = y-intercept.
(2) Parallel lines have equal slopes.
Transform $2x+3y+4=0$ to slope-intercept form to obtain:
$2x+3y+4=0
\\3y=-2x-4
\\\dfrac{3y}{3}=\dfrac{-2x-4}{3}
\\y = -\dfrac{2}{3}x -\dfrac{4}{3}$
The slope of this line is $-\dfrac{2}{3}$.
The line we are looking for the equation of is parallel to the line above.
Thus, the slope of the line is also $-\dfrac{2}{3}$.
This means that a tentative equation of the line is:
$y=-\dfrac{2}{3}x+b$
The y-intercept of the line we are looking for is $6$.
This means that $b=6$.
Therefore, the equation of the line we are looking for is:
$y=-\dfrac{2}{3}x +6$
