Intermediate Algebra (12th Edition)

(a) $y=\frac{2}{3}x+8$ (b) $2x-3y=-24$
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 ($Ax+By=C$): $y=\displaystyle \frac{2}{3}x+8$ $3*y=3(\displaystyle \frac{2}{3}x+8)$ $3y=2x+24$ $-2x+3y=24$ $2x-3y=-24$