The slope of a position-time graph provides insight about the velocity of the object. By carefully interpreting the slope of the line and how it changes over time, one can determine the manner in which the object is moving - constant speed, speeding up, slowing down, and the direction of motion.
 

You have to match the motions of A, B, and C to one of the six lines on the position-time graph. That's going to require some good thinking and decision-making. The following should help:

Positive vs. Negative Velocity: For each object, you need to decide whether the velocity is positive or negative. Look at the arrow on the dot diagram; it indicates the direction that the object is moving. Typically a leftward motion is considered a negative velocity and a rightward motion is a positive velocity. A positive velocity is represented by a line with positive slope and a negative velocity by a line with negative slope.

Fast vs. Slow: The three objects have different speeds. The amoiunt of space (distance) between adjacent dots reveals the speed. A large spacing corresponds to an object with high speed. Match this object to the line with the greatest slope since the steepest line - whether upward sloped or downward sloped - corresponds to the fastest object. In a similar manner, match the object with the smallest speed to the line with the smallest slope.