1. I NTRODUCTION TO L INEAR F UNCTIONS

2. W HAT IS A L INEAR F UNCTION ? A linear function is a function whose graph is a straight line. A linear equation has a graph with a straight line (It might not be a function…). This is not a function, but it is a straight line!

3. A RE THESE LINEAR ? No Yes

4. H OW DO WE TELL FROM A TABLE ? The rate of the ratio of the changes of y’s to the change in x’s must be constant (the same). Example: xf(x) 00 13 39 412 +3 +6 +3 +1 +2 +1 m = change in y’s change in x’s The rate of change is the same so the relationship represented by the table is linear.

5. xf(x) 23 35 48 617 A RE THESE LINEAR ? +1 +2 +3 +9 m = change in y’s change in x’s The ratios are different so the relationship represented by the table is NOT linear. xf(x) -158 -52 0 10-7 +10 +5 +10 -6 -3 -6 m = change in y’s change in x’s The ratios are the same so the relationship represented by the table is linear.

6. H OW DO WE TELL FROM AN EQUATION ? No variable can have an exponent greater than 1. No exponents greater than 1 so…YES it’s linear! An exponent is greater than 1 so…NO it’s not linear! No exponents greater than 1 so…YES it’s linear! An exponent is greater than 1 so…NO it’s not linear!

7. I S IT L INEAR ? S ORTING A CTIVITY Cut apart the cards. Separate them based on if they are linear or not linear.