1. Bean Investigation Presentation By:Serhiy Smirnov Period:1

2. Sketch of Terms 0-3 Term 0 Term 1 Term 2 Term 3

3. Rate of Change Term 0 has 7 beans and each time there is a different term, the number of bean increases by 5 beans so in term 1 there will be 12 beans and in term 2 there will be 17 beans and so on.

4. Table of terms 0-6 Term #Total # of beans 07 112 217 322 427 532 637

5. Algebraic Rule (Equation) My algebraic rule for my pattern is: 5x+7=y because you multiply the term # by 5 and then add 7 to the term number and you get your total number of beans.

6. Color coded sketch of Term 0-3 Term 0 Term 1 Term 2 Term 3

7. Connection between green beans and rate of change For every new term, 5 beans are added to the pattern. There are 7 beans in the first term so there are 5 more beans in term 2 so there are 12 beans in the 2nd term and 17 in the third term and so on.

8. Color coded sketch of original beans

9. Connection between red beans and y- intercept The y-intercept is the number of original red beans in the pattern.

10. Slope intercept formula y=mx+b ●M represents the slope(rate of change) in the formula ●B represents the y-intercept in the formula

11. Equation for linear pattern 5x+7=y My equation makes sense for my pattern because you multiply the term # by 5 and then add 7 to the answer to get the total number of beans in that term.