Should the 50- and 200-day moving average lines be considering a stock breaking out of a base?

Not necessarily. In some cases, when a base is predominantly horizontal in shape, the moving average lines can be more or less flat. But rather than looking at the slope of the moving average lines, you should check if the stock is above its 50-day moving average. If it isn’t, chances are there is something wrong with the breakout. Also, you’ll sometimes see the 50-day moving average cross above the 200-day line at about the same time of the breakout, although this crossover is not by itself a signal to buy. Overall, the overriding factor in studying any breakout is the health of the base pattern. Moving averages are just a secondary indicator.