ok, the general equation of a line is y=mx+c, with m being the gradient, and the c being the y-intercept. so you already know that the line would be y=-4x+c. They told you a point on the line, so you subt that in. With x being -6, and y being 7. So, you should get 7=(-4)(-6)+c. Now you should be able to find c, which is -17. so the equation is y=-4x-17.
