What are the basic differences between the uphill and downhill parts on a position graph? How do the different signs of the velocity during the two parts manifest themselves in the changing slope of the position graph?

A positive slope reveal that the line goes uphill, from low to high. whereas negative slope tells us that the line goes downhill, from high to low.

Slope is calculated as change in the vertical direction (y) ÷ change in the horizontal (x); this is often called rise over run.

To find the slope you can pick two points on the line and find the difference in the y values, and divide it by the difference in the x values. The important thing to remember is to keep the points in the same order in the numerator and denominator.