Answer
(a) $y=\frac{2}{3}x+8$
(b) $2x-3y=-24$
Work Step by Step
A line in point-slope form has the equation:
$y-y_1=m(x-x_1)$
We use the given point $(-3,6)$ and slope $m=2/3$:
$y-y_{1}=m(x-x_{1})$
$y-6=\frac{2}{3}(x--3)$
$y-6=\frac{2}{3}(x+3)$
$y-6=\frac{2}{3}x+2$
$y=\frac{2}{3}x+8$
Now the line is in slope-intercept form ($y=mx+b$).
(b)
We convert to standard form ($Ax+By=C$):
$y=\displaystyle \frac{2}{3}x+8$
$3*y=3(\displaystyle \frac{2}{3}x+8)$
$3y=2x+24$
$-2x+3y=24$
$2x-3y=-24$
