University:
College
Course:
College Mathematics
Academic year:

2023
Views:

391

Pages:

2
Author:

J. Lay

Recognizing Linear Patterns The First step to recognizing a Pattern is to arrange a set Of numbers in a table. The table can be either horizontal or vertical. Here, we Consider the Patern in a horizontal format. more advanced analysis generally uses the vertical Format. Consider this pattern: x-Value To analyze the pattern, we calculate differences of successive Values in the table. These are called first differences. If the First differences are constant, we can proceed to Converting the Pattern into an equation. If not, we do not have a linear Pattern. In the case, we may choose to continue by calculating differences of the First differences, which are called second differences, and so on until we get a Pattern we can work with. In the example above, we get constant Set of first differences, which tell us that the pattern is indeed linear. X-Value Y-Value Converting a Linear Pattern to an Equation * Creating an equation From the pattern is easy if you have Constant differences and y-Value For x = 0. In the case, - The equation takes the Form y=mx+b, where - "m" is the Constant difference From the table, and "b" is the y-value when Xx.0. Wote: If the table does not have a Value for X. O, yo can still Obtain the value of "b". Simply extend the table left or right until you have an x-value of O; then use the first differen Ces to calculate what the corresponding Y-Value would be. this becomes your value for "b" In the example above, this gives use the equation: Y = 3X+6 Finally, it is a good idea to test your equation, For example, IF X-4. the above equation gives Y = (3.4)+6= 18, which is the value in the table. So we Can be pretty sure our equation is Correct.