Linear vs Non Linear RELATIONS Sets of Data

Linear vs. Non Linear:

RELATIONS (Sets of Data) FUNCTION One output for each input LINEAR Common difference / straight line NON - LINEAR

Linear or Non-Linear Only functions are linear. For a function to be linear, there has to be a common difference – this means to look at the outputs, and if you get the same solution when you subtract, you have a common difference. Linear functions, when graphed, form a straight line.

Graph: **It means formed by a line **These linear equations look like a line when graphed Linear Non-Linear

Table: To determine if a table has a linear relationship, look for a common difference (SLOPE). x 1 2 3 4 y 3 6 9 12 CD: 3 x 4 5 6 7 y 16 25 36 49 CD: no

� Common difference for the y’s is adding 3 each time to get to the next y. � Common difference for the x’s is adding 1 each time to get to the next x. � Common difference is y/x, so 3/1=3, so function is linear. � 2 nd problem common difference of y’s is not always the same, so this function is not linear.

Equation: � 3 checks = LINEAR

Is it Linear? ? *When looking at a graph, graph if it makes a straight line, IT’S LINEAR. *When looking at a table, table if there is a common difference, IT’S LINEAR. *When looking at an equation, equation if there are no exponents, no variables multiplied together, and no variables in the denominator, IT’S LINEAR.

Ticket Out The Door… On your sticky note, write down if you think the following functions are LINEAR or NON - LINEAR

*No Exponents *No variables being multiplied together *No variable in denominator 2 a + 3 b = 4 y = 5 x – 3 xy y=1 x A = s 2

2 a + 3 b = 4 LINEAR y = 5 x – 3 xy NON - LINEAR y=1 x NON - LINEAR A = s 2 NON - LINEAR