I see value in measuring the slope is it that in the end of the trend, the short term slope would be flat or inverse of the longer term slope before the two crosses over. Otherwise, in the middle of the trend, both should be upward sloping (assuming rising trend).
In reading your comments and questions a glaring omission became painfully clear (this is probably a bit of an overstatement) which I would like to correct at this time—which was my failure to mention that my description then (and what will now follow) is not, technically speaking, precisely accurate language.
But first, let me admit that I cannot answer your question on ticks. I am not clear on exactly what a tick is. Every time I read up on the topic, the definition of the term fades from memory soon after. Moreover, when I study tick charts, I feel what I am looking at does not match (accurately reflect) what is going on in reality. The result of such episodes is that my motivation to look into ticks more deeply is nonexistent.
You commented that “in time based charts, slope is (y2-y1)/(X2-X1) where it is essentially the change of price vs. time.”
This reflects my understanding of slope, but when it came to representing this on MT4 candlestick charts, I was unable to devise a valid means of doing so. I thought perhaps a rate of change (ROC) indicator might do the trick, but in trying to apply its use, I found that it did not turn out to be practical for me personally.
The closest I could get to something anywhere near what I might view as functional was to divide a moving average in its present state with where it was at some time in the past. Most recently, I was choosing to divide it by where it was one period ago. The resulting indicator (oscillator) was above zero when the moving average was headed north, and below zero if the moving average was headed south. Unfortunately, this too I did not find to be of great practical use.
With respect to your assumption that one of the moving averages is short-term and the other is long-term, this would depend on how you define these two expressions.
In one sense,
both of the moving averages I use to dictate when I enter and exit positions are short-term moving averages. The longer/slower of the two is the one I regard as tracking the intraday trend with the greatest amount of precision, validity, and accuracy possible without subjecting a trader to head fakes or false positives.
The shorter/quicker of the two conveys the shortest-term trend by measuring price direction in the smallest possible
meaningful units, and is therefore extremely accurate, but also subject to frequent fluctuations, so cannot really be trusted as an “actionable” indicator.
What I do is compare the faster indicator to the slower one, but the slower one is actually pretty fast itself. So then, I am not really measuring the slope of either trendline. In the language you used in your initial post, I am measuring the
difference of the two SMA periods (by dividing the faster moving average by the slower one).
Because they are both accurate measures of
short-term trend, when they are moving in tandem with one another, it leaves little doubt as to which direction price is headed from an intraday point of view. One might think of them as confirming each other, and when this is the case, the momentum in the given direction is quite significant.
When the faster indicator begins distancing itself from the "slower" one (relatively speaking) there is still no question about which direction price is headed, but momentum is increasingly extreme and on its way to becoming unsustainable.
Technically, your comment about the short-term slope being flat or inverse of the long-term slope before the two cross over is correct, but because the two moving averages I use are not that far apart, this is not what usually happens.
More common is for the two of them to reverse direction almost simultaneously, as represented in the image I posted where the two of them were trending south before reversing direction to trend north.
The second most common occurrence is for the fast line to pull away from the “slow” line in the same direction of the intraday trend or opposite the direction of the intraday trend, then reverse direction to move
back to the “slow” line, and reverse direction again (or decreased its radical slope) to more-or-less
rejoin the “slow” line in its general trajectory, whichever direction that might happen to be.