1. Directly Proportional Vs. Linear TicketsPeople 31 62 93 124 TicketsPeople 32 63 94 125 TABLE 543210543210 0 3 6 9 12 PEOPLEPEOPLE TICKETS PEOPLEPEOPLE 543210543210 0 3 6 9 12 TICKETS

2. Directly Proportional TicketsPeople 31 62 93 124 TABLE 543210543210 0 3 6 9 12 PEOPLEPEOPLE TICKETS Both variables increase at a Constant (k) Rate. Divide y & x to find a Constant (k) in order to test for Directly Proportional Relationships within a table. Only 2 items in the relationship. Starts at the origin.

3. Linear Relationship Check to see if table has a pattern, but DOES NOT divide to give a Constant (k). DOES NOT start at the origin. Has an extra variable/flat rate. Starts at the y-intercept. TicketsPeople 32 63 94 125 GRAPH PEOPLEPEOPLE 543210543210 0 3 6 9 12 TICKETS

4. Graph/Table Linear Equation Nachos$ (Money) 04 210 416 622 Table $ Nachos 22 20 18 16 14 12 10 8 6 4 2 0 0 2 4 6

5. Inversely Proportional MilesHours 1201 602 403 304 GRAPH 5 4 3 2 1 05 4 3 2 1 0 10 20 30 40 50 60 70 80 90 100 110 120 X variable increase, Y variable decreases or Vice Versa at a Constant (k) Rate. Multiply x & y in the table to find a Constant (k) to test for Inversely Proportional

6. NonLinear

7. TABLES Flow Chart for Testing BAGSAPPLES 17 211 315 419 CHECK FOR SLOPE/PATTERN YES NO ALL RATIOS EQUAL RATIOS NOT EQUAL DIRECT LINEAR MULTIPLY X & Y (K) CONSTANT ALL THE SAME (K) CONSTANT NOT THE SAME INVERSE NONLINEAR

9. Practice XY 25 410 615 820 1) 3) 2) 4) XY 224 412 68 86 XY 16 210 314 418 XY 12 35 512 718 Directly Proportional? Linear? Nonlinear? Inversely proportional?

10. Practice Miles traveledCost of gas 25$5 50$10 75$15 100$20 1) 3) 2) 4) Miles traveledCost of gas 25$5 50$10 75$15 100$20 302 601 90 Miles traveledCost of gas

11. CHECK FOR PATTERN YES NO ALL RATIOS EQUAL RATIOS NOT EQUAL Directly Proportional LINEAR MULTIPLY X & Y (K) CONSTANT ALL THE SAME (K) CONSTANT NOT THE SAME NONLINEAR Inversely Proportional

12. YES NO Draw these and fill these in on the quiz!!!

13. Review for quiz Tell if each table is linear, nonlinear, directly proportional, or inversely proportional. 1) 2) 3) 4) XY 124 212 38 64 XY 304 608 9012 1204 XY 520 1040 1560 2080 XY 511 613 715 817

14. Review for quiz

15. Practice