Parallel lines have the same slope [tex]m[/tex] and never coincide. So to write a line that passes through the given point and has slope -2, it is helpful to write this into point-slope form, [tex]y-y_1 = m(x-x_1)[/tex]. We use the given point, (-3, -4). Substituting this in, we get [tex]y - (-4) = -2(x-(-3))[/tex], or [tex]y + 4 = -2(x+3)[/tex]. Now, you should distribute the -2 and subtract four from both sides to get this into slope-intercept form, [tex]y = mx+b[/tex]. Doing that, you get [tex]y = -2x -10[/tex].
You can verify that it indeed satisfies the requirements because (-3, -4) is a solution of the equation. [tex]-4 = -2(-3) -10 = -4[/tex]
