1. The given line has the equation

2. If the normal to the curve has the slope m = 3 then the curve must have the gradient

3. That means

4. The normals with m = 3 have to pass through the points P(-3, -1) and Q(3, 1).

Use the point-slope-formula of the straight line to get their equations.

5. The given line: green. The 2 normals in red: