Increasing or Decreasing Pattern 

Definition

Consider a table of values; represented by an independent variable (x) and a dependent variable (y). We often use atable of valuesto display the values we record. Using the table, we can find the relationship between the two variables and write it as a rule. There may be an increasing or decreasing pattern in the relationship between the two variables.

Example

Consider that the total cost (y) of x items is two times the no of items, i.e., y =2 x. The total cost (y) increases as the number of items (x) increase. So it is clear that there is an increasing pattern here in the values of the variables.

Problem 1

Consider the values of the variables in the table given below.

Solution

Step 1:

Consider pairs of consecutive x values and find the difference.

4 2 = 6 4 = 8 6 = 10 8 = 2

Step 2:

Similarly consider pairs of consecutive y values and see the difference.

9 7 = 11 9 = 13 11 = 15 13 = 2

Step 3:

We find that for 2-unit increase in x, there is a 2-unit increase in the y value. So we see an increasing pattern in this table of values.

Problem 2

Consider the values of the variables in the table given below.

Solution

Step 1:

Consider pairs of consecutive x values and find the difference.

5 2 = 8 5 = 11 8 = 14 11= 3

Step 2:

Similarly consider pairs of consecutive y values and see the difference.

4 6 = 2 4 = 0 2 = -2 0 = – 2

Step 3:

We find that for 3-unit increase in x, there is a 2-unit decrease in the y value. So we see a decreasing pattern in this table of values.