How do latitude and altitude affect which plants grow in an area?

They are both important. Latitude, the lines that parallel the equator are very important in determining plant growth rates and which plants can even exist because latitude is strongly related to average temperature. Altitude acts like latitude only over a shorter scale, so an increase in altitude of 1,000 ft may act like a latitude change of 3-4 degrees pole-ward. Longitude, that series of lines, perpendicular to the equator is also important, and is more related to water supply in the form of precipitation, so it would surely influence the kind of plants present - like desert plants versus rain forest types. Environments that are warm and with more rainfall generally will support more plant growth than those that are cold with little rainfall.