Answer
$y=-\dfrac{2}{3}x+6$, or, in general form, $2x+3y-18=0$
Work Step by Step
$y$-intercept $6;$ parallel to the line $2x+3y+4=0$
Use the slope-intercept form of the equation of a line, which is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept.
The $y$-intercept and the equation of a line parallel to the one to be found are given.
Solve the given equation for $y$. The resulting expression will be in slope-intercept form and the slope $m$ will be the number in front of $x$:
$2x+3y+4=0$
$3y=-2x-4$
$y=-\dfrac{2}{3}x-\dfrac{4}{3}$
The slope of the given line is $-\dfrac{2}{3}$
Since the line whose equation must be found is parallel to the line whose equation is given, then the slope of the first is also $-\dfrac{2}{3}$
Substitute the $y$-intercept given and the slope into the slope-intercept form of the equation of a line formula and simplify to obtain the answer:
$y=mx+b$
$y=-\dfrac{2}{3}x+6$, or, in general form, $2x+3y-18=0$
