What is the best way to evaluate the risk of an avalanche occurring on a slope?
You can use the following three questions as a guide to help you decide where and why an avalanche can occur

1. Is the snow unstable and where is it unstable?
    Unstable snow is snow that wants to or can slide downhill. Weather, precipitation, temperature, wind, sun and many other factors influence snowpack stability. While it takes more formal training and experience to understand and analyze snowpack conditions, there is one easy way to get this information: Read the avalanche forecast to find out whether the snow is unstable and where.

    Avalanche forecasters and other professionals make field observations and analyze the snowpack and weather over the season to help you make decisions about when and where to go. These forecasts alert you to avalanche dangers and explain the types of problems you might expect.

2. Am I in terrain where avalanches can occur?
    Recognizing avalanche terrain (where they occur) is a key to traveling safely in the backcountry. Avalanche terrain is anywhere an avalanche can start, run or stop. Learn to recognize such terrain to help you plan a trip and pick a safe route.

    Consider these factors when deciding whether you’re in avalanche terrain:

    - Steepness of the slope: A slope has to be steep enough for snow to slide. Most avalanche activity typically starts on slopes between 30 and 45 degrees. Some slides can happen on lower angles but they’re not common. As you travel in the backcountry, ask yourself whether the slope is steep enough for snow to slide. It can be hard to estimate slope angle; a slope meter (inclinometer) is a useful tool to measure slope angle quickly. (Practice using a slope meter at a ski resort or elsewhere before traveling into the backcountry.)
    - Connected slopes: Avalanche terrain is anywhere an avalanche can start, run and stop. If you’re traveling in more gentle terrain but it’s connected to steeper slopes above you that can slide, there’s still a risk of an avalanche. 
    - Terrain traps: These are features like gullies, rocks, cliffs, trees or crevasses that can magnify the consequences of an avalanche. If you get caught in an avalanche, terrain traps will make even a small slide worse because they increase the risk of injuries or make it more challenging to dig someone out. A small slide can cause traumatic injuries if it barrels you into hard objects such as trees or rocks, sends you off a cliff, or buries you deeply in a gully or depression. Most people who die in avalanches do so from asphyxia (typically because they’re unable to breathe when buried) or trauma.

3. Can I trigger an avalanche?
    The third factor needed for an avalanche to occur is a trigger. Natural triggers such as snow, wind or rain can cause avalanches. But most avalanche accidents are triggered by the subsequent victim or someone in the victim’s group. A skier, snowboarder, snowshoer, snowmobiler, climber and others can all trigger avalanches (such as by moving their weight over unstable snow). So the decisions you make about when and where to go and how to travel can make a huge difference in preventing accidents. And despite a prevailing myth, you cannot trigger an avalanche by shouting or making loud noises.
Write a tldr summary.
TLDR:
1. Is the snow unstable or likely to shift?
2. Are the slope conditions conducive to an avalanche? If an avalanche were to occur would the most likely path endanger anyone or anything?
3. Is a trigger likely to be present? There are many possible triggers including the buildup of snow, or snow sport enthusiasts accidentally triggering one.