Linear vs. Non Linear:

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

Only functions are 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 6 9 12 x 4 5 6 7 y 16 25 36 49 CD: 3 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. 2nd problem common difference of y’s is not always the same, so this function is not linear.

Equation: If you want to check if an equation is linear, use the check list: NO exponents x3 No variables being multiplied together 6xy No variables in denominator 𝟑𝐱 𝐲 3 checks = LINEAR

Is it Linear?? *When looking at a graph, if it makes a straight line, IT’S LINEAR. *When looking at a table, if there is a common difference, IT’S LINEAR. *When looking at an 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

2a + 3b = 4 y = 5x – 3xy y = 1 x A = s2 *No Exponents *No variables being multiplied together *No variable in denominator

2a + 3b = 4 LINEAR y = 5x – 3xy NON - LINEAR y = 1 x A = s2