Trendlines do not predict levels of support and resistance. Support and resistance run horizontally; not at an angle. For an explanation of the basics, see Support and Resistance. Many traders confuse the two concepts: the lower line in a trend channel is often referred to as the supporting trendline.
Highs or Lows
On a short-term chart (6 months or less), draw trendlines through the lows during an up-trend.
And through highs during a down-trend.
On a long-term chart, trendlines drawn with closing price are more effective.
There has been much debate on the Chart Forum over the years as to whether trendlines should be drawn on log scale or normal scale charts.
The case for log scale has been summarized by Alsoran as:
- Brokers and analysts chart in log mode. They advise institutional clients whose order flow has a marked impact on price action and trend. Their advice is heavily influenced by breaks and refusals of price at key trendlines and channels. These are based on logarithmic charts. Logarithmic trendlines are, therefore, more important.
The case for normal scale (linear) trendlines:
- Most trading authors use linear charts: Stan Weinstein, Alexander Elder, Chris Tate and Daryl Guppy.
- It is questionable whether most analysts and brokers use log scale charts. Many trading authors (including Stan Weinstein and Chris Tate) are former analysts or brokers and use linear charts.
In my opinion the two sides are talking about different time frames!
Normal scale charts compare price against time. You would graph the speed of a car in a similar manner: distance (y) over time (x). If a car travels at a constant velocity, the graph will be a straight line. If stopped, the line will be horizontal. If accelerating, the graph will show a curve.
Log charts are not designed to measure velocity, they measure acceleration: the rate of growth in stock prices. A constant velocity will be depicted as a flattening curve; a constant rate of growth (acceleration) will be depicted as a straight line.
In the short/medium term we focus on velocity: "Is this week's price increase as good as last week?" The time period is too short to be concerned with compound growth rates.
Most institutions hold instruments for the long-term and do not concern themselves with short-term fluctuations. They want to know the annual compound growth rate; a very different concept from short-term velocity.
- On short-term and medium-term charts (3 years or less) we recommend that you use normal scale.
- For long-term charts (more than 3 years), use either normal scale (linear) or log charts, but be aware of their respective strengths and weaknesses. Personally, I prefer to draw trendlines on linear charts unless we are looking at a 10 or 20 year time period.
Linear trendlines appear to accelerate over time if a instruments grows at a constant compound rate with variations of some descelerate.
Logarithmic trendlines more accurately present the rate of growth (or decline) over very long time periods.
Let's take a look at some of the basics in more detail.
What do we mean by respect? Price should reverse in close proximity to the trendline but not cross it. 
Short-term charts often display candles with long tails or shadows when stops are shaken out, or traders get caught in a false break, initiated by market professionals. If the daily high or low gets in the way of an obvious trendline -- ignore it, but do not intersect closing prices.
Avoid intersecting closing price except on a long-term chart if there is a spike that does not fit the overall pattern. And only do so in exceptional circumstances: the trend must really be obvious.
Trendline breaks signal a change in momentum; not necessarily a change in trend. Trendline breaks often look obvious with hindsight, but you will normally find that the trendline depicted was not the first one drawn: several trendlines may be broken before there is a trend reversal.
- If trading short-term or swing trading, act upon trendline breaks when you receive price confirmation (or confirmation from another indicator), as you would for any other momentum indicator.
- In the longer-term, trendlines are an effective tool for exiting trends that have spiked into a blow-off (or down-trends that have spiked into a cathartic sell-off).
Draw trendlines through the lows in an up-trend and through the highs in a down-trend. Use closing price for longer-term charts (more than 6 months). Use normal scale for short and medium-term charts. Use either normal or log scale for long-term charts but beware of their weaknesses.
Valid trendlines must be respected by at least 3 troughs in an up-trend (or 3 peaks in a down-trend) and should not intersect the closing price line if extended in either direction. Use trendlines as a momentum indicator for short-term trades but only as an alert on long-term trades. They are also an effective exit tool for blow-offs.
Don't waste time drawing trendlines on every chart. They are time-consuming and should only be drawn on a handful of selected instruments.
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