Line charts are based off of closing prices, thus, in order for a (insert given time unit) chart to bottom, the next time unit would have to close higher.
So, to be extremely clear, a better way of communicating what I mean (in that it would be more consistent) would be to phrase it like this: "my expectation is and has been that June will be the montly bottom on a line chart, thus, if proven correct would mean July will close higher than it started"