Answer
$y = -\frac23x + 6 $
Work Step by Step
We are told to find the equation of the line that satisfies the following conditions:
$y$-intercept is 6, and parallel to the line $2x + 3y +4 = 0$
To find the equation of the line we must find the slope
then write it in the form:$ y =mx + b$
First solve the given equation for $y$:
$2x + 3y + 4 = 0$
$3y = -2x - 4$
$y = -\frac{2}{3}x - \frac{4}{3}$
Since the lines are parallel they have the same slope, so the slope of our equation is $m = -\frac23$
$b = 6$
$y = -\frac23x + 6 $
