1. Warm Up – January 12 from Friday’s Quiz   You must be older than 10 to take this quiz.   Sally said that the inequality statement should be p>10, but John said that the inequality statement should be 10>p. Who is right? Why?   Quizzes returned. Questions?

2. Homework Tonight!  Write in your agenda!  Pages 494 and 499 of the textbook.

3. Today’s Standard and Learning Target   MCC6.EE.9 : Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.   Learning Target: I can show relationships between two variables (independent and dependent) using an equation, a table and a graph.

4. Variation and Proportion y = kx Direct Proportion Page 138 of your MSG

5. The formula for direct variation can be written as y=kx where k is called the constant of variation.   The steps to follow to solve a problem with direct variation: 1. 1. Write the equation: y = kx 2. 2. Substitute for x and y 3. 3. Solve for k 4. 4. Rewrite the equation with k as the constant

6. Problem: Find an equation of direct variation where y varies directly as x. One pair of values is y = 7 when x = 35. 1. 1. Write the equation: y = kxy = kx 2. 2. Substitute for x and y7 = k(35) 3. 3. Solve for k7/35 = k, or k = 1/5 4. 4. Rewrite the equation with k y = 1/5x as the constant

7. Problem: The cost of operating a TV varies directly as the number (n) of hours it is in operation. It costs $15.00 to operate a standard size color TV continuously for 30 days.   y = cost; x = number of hours 1. 1. y = kx 2. 2. 15 = k(30) 3. 3. 15/30 = k, or k = 1/2   Equation: y = 1/2x or y =.5x

8. Practice Problems: Answers 1. y = 28 when x = 7  Equation: y = 4x 2. y = 30 when x = 8  Equation: y = 15/4x 3. y = 625 when x = 125  Equation: y = 6x 4. y = 630 when x = 175  Equation: y = 18/5x

9. Practice Problems: Answers (Continued)

10. Putting It Together – Page 139 MSG  Fill in the blanks. Discuss!

11. Study Jams- Function Tables Preview!  http://studyjams.scholastic.com/studyjams/ jams/math/algebra/function-tables.htm

12. Page 140 of MSG  1) Rule: y = 35x  2) $7.50 per chore: y = 7.5x X (# of tickets) 02346 Y (cost) X (# of chores) 02101550 Y (total $ earned)

13. Page 140 Continued!  3) 37 boys are in the drama club. They are going to pitch in the same amount to buy new props. X (amount $ each boy brings) 023510 Y (total $ raised)

14. Page 499 of textbook Examples! (HW)  Input and output function tables:  #1)  #5) Input (X)3x + 5Output 0 3 9 Number of guests (x) 30 ÷ xCupcakes per Guest (y) 6 10 15

15. Closing – What is direct proportion?  When you catch the ball, state one thing that you have learned today about direct proportion or about function tables! What new vocabulary have we learned?