## Calculus: Early Transcendentals 8th Edition

$y = -\frac23x + 6$
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 $m = -\frac23$ $b = 6$ $y = -\frac23x + 6$