The slopes of two parallel lines must be identical.
We have slope [tex]m=3[/tex], so the slope for the parallel line be the same.
Now, to find an equation that also passes through the given point, we use slope-point form, [tex]y-y_1=m(x-x_1)[/tex], where our point [tex](-4,-3)[/tex] is substituted for [tex](x_1,y_1)[/tex].
[tex]y+3=3(x+4)[/tex]
Now, we convert to slope-intercept form as such.
[tex]y=3x+12-3\\y=3x+9[/tex]
And we are done. :) We can verify graphically that these are indeed parallel lines. See attached.
