The point P(-3,9) belongs to a line intercepting the origin. Find the equation of the line.

We are told that the line passes through the origin O (0,0) and the point P (-3,9). First we need to find the gradient of the line m; this is given by m = (change in y)/(change in x), hence m = (9-0)/(-3-0) = 9/-3 = -3. The general equation of a line is y = mx+c. Because the line intercepts the origin c = 0, hence the equation of the line is y = -3x.