Patterns in Graphs
Two quanties may have a range of relationships. Usually the best way to establish a relatioship is to plot a graph of one quantity against the other. Possible relationships between two quantities are shown below.


x and y are directly proportional. We can write y=kx where k is a constant of proportionality.  There is a linear relationship between x and y. We can write y=mx+c 


x and y increase together but are not linearly related.  If x increases y decreases and vice versa. There is no linear relationship between x and y. 


There is a negative linear relationship between x and y. We can write y=mx+c where m is negative.  There is a negative relationship between x and y but the relationship is not linear. If x increases, y decreases and vice versa. 