Question

What is the parallel to 2x-3y=6 and passing through(-3,1) ...?

Answer 1

Parallel lines have equal slopes.

$2x-3y=6 \\-3y=-2x+6 \\ \\y= \frac{2}{3} x-2 \\ \\m= \frac{2}{3} \\ \\(-3,1) \Rightarrow x_1=-3,y_1=1 \\ \\y-y_1=m(x-x_1) \\ \\y-1=\frac{2}{3}(x-(-3)) \\ \\y-1=\frac{2}{3}(x+3) \\ \\y-1=\frac{2}{3}x+2 \\ \\3y-3=2x+6 \\ \\2x-3y+9=0$