Altitude 6450 feet Runway 6300 feet max Temperature 75° F Barometric Pressure 30.2
These factors interact. Here's a chart I constructed from a variety of sources, to try to illustrate the details. These are not exact, but I'm sure no pilots will plan a flight with this, as they will be calculating a much more precise figure known as Density Altitude.
The orange dotted line shows a full load take-off at sea level and 70° F requires about 4500 feet of runway. Now look at the green and raspberry dotted lines. You can see as the altitude increases so does the minimum runway length.
The yellow and yellow/green lines show the maximum loads at 6500 feet altitude for different temperatures. Jackson has a short runway, and we need a margin for error. The red spots show how the maximum passenger capacity changes with temperature.
One quick rule of thumb for a small plane is 200 lbs change in payload equals 500 feet of runway.
Now why does all this math matter?
When we checked in, we learned that due to weather and altitude, capacity had to be restricted to 55 passengers. The airline had booked more than 70, expecting a few no-shows. But more than 70 had already checked in, so at least 15 people would miss the flight.
We didn't. In 2 million miles of flying, this has happened to me before. I quickly asked to change to an earlier flight, and we got home with no problems.