1. Name:________________________________________________________________________________Date:_____/_____/__________ Solve the following linear equations (plug x into equation): 1)2) xy = -2(x + 1)y 0 1 2 xx = y - 4y 0 1 2 Write the equation for the following function tables (magic #): 3) Equation:____________ 4) Equation:____________ 5) Equation:____________ xy 04 19 214 xy 04 11 2-2 3-5 xy 829 933 1037 1141 Fill-in-the-blank: 6)y = m x + b is the formula for writing a linear equation in ________________________________ form. 7)The “m” stands for _________________. 8)The “b” stands for the _______________________.

2. Graph the following equations (use y = mx + b ): 9) y = -3x + 8 ( m = _____; b = _____ ) Study graph and write the equation (use y = mx + b): 11) m = _____ b = _____ Equation:__________________________

3. Math-7 practice DATE: ______/_______/_______ NAME:__________________________________________________________________________________ “SLOPE-intercept form”

4. m = _____ b = _____ m = _____ b = _____ m = _____ b = _____ m = _____ b = _____ m = _____ b = _____ m = _____ b = _____ m = _____ b = _____ m = _____ b = _____

5. Today’s Lesson: What: Representing a function Why: To make connections among the four ways to represent a function. What: Representing a function Why: To make connections among the four ways to represent a function. Input Output

6. Do you remember the 4 ways to represent a function??: y = 2x + 3 With words “y is equal to ------------------------- ---------------------” As a __________ 2 xy 0 1 2 3 3 As a graph 4 As an ____________ 1 Equation Table 3 5 7 9 two times a number plus three. Now, plot the points!

7. EquationWords 1) y = 2x -1 TableGraph xy “y is equal to the product of two and a number, minus one.” 0 1 2 3 1 3 5 let’s tie it all together... From an equation... b = -1

8. EquationWords 2) “y is equal to three more than a number.” TableGraph y = x + 3 xy 0 1 2 3 3 4 5 6 From words... You could use y= mx + b to graph OR you could create the table by choosing inputs and plugging in... Now, plot the points!

9. EquationWords 3) TableGraph xy 06 14 22 30 From a table... y = -2x + 6 “y is equal to negative 2 times a number, plus six.” Magic Number...

10. EquationWords 4) TableGraph From a graph... xy 0 1 2 3 4 2 0 -2 y = -2x + 4 “y is equal to four more than negative 2 times a number.” b = 4

11. END OF LESSON The next slides are student copies of the notes and/or handouts for this lesson. These were handed out in class and filled-in as the lesson progressed.

12. Math-7 NOTES DATE: ______/_______/_______ What: representing functions Why: To make connections between the four ways to represent functions. What: representing functions Why: To make connections between the four ways to represent functions. NAME: Do you remember the 4 ways to represent a function??: y = 2x + 3 With words “ y is equal to ------------------------- ---------------------” Of course you remember! 2 xy 0 1 2 3 3 As a graph 4 As an _____________ 1 If you are given one of the above representations, you need To be able to represent that function in the other 3 ways! As a ___________

14. Matching representations activity

15. EquationWordsTableGraph 1) y = 2x - 2 “y is equal to the product of 2 and a number, minus 2.” 2) y = -3x + 1 3)“Four plus a number is equal to y.” 4)“ y equals negative x.” xy 0 1 2 xy 0 1 2 3 xy -3 0 3 6 xy 0 1 2 3 Math-7 homework NAME:________________________________________________________________________________ DATE: _____/_____/__________ “Function representations” Apply everything we have learned in this unit in order to fill in blank spaces:

16. EquationWordsTableGraph 5) 6) 7) 8) xy -3 01 15 29 xy -27 4 01 1-2 xy xy Magic #... y = mx + b

17. Math-7 classwork DATE: ______/_______/_______ NAME:__________________________________________________________________________________ “Linear Equation applications” It is midnight in Leesburg and there is no snow on the ground. It begins to snow at a rate of 2 cm each hour. Create a table that shows the amount of snow on the ground for every hour after midnight until 5 am. (Hint: use 0 to represent midnight) Graph the equation using your table of values: Write an equation to represent this situation. Equation:____________________________________ If it continues to snow at the same rate, how much snowfall would there be at 10 am? At midnight in Chicago there are 4 cm of snow on the ground. It begins to snow at a rate of 3 cm per hour. Create a table that shows the amount of snow on the ground for every hour after midnight until 5 am. Graph the equation using your table of values: Write an equation to represent this situation. Equation:____________________________________ If it continues to snow at the same rate,. How much snowfall would there be at 2 pm (14:00)? xy 0 1 am xy 0

18. Draw and extend the following pattern: Create a table that shows the relationship between the figure number and the number of toothpicks in each figure. Graph the equation using your table of values: Write an equation to represent this situation. Equation:_________________________________________ How many toothpicks will be in the 75 th figure? Draw and extend the following pattern: Create a table that shows the relationship between the figure number and the number of square blocks in each figure. Graph the equation using your table of values: Write an equation to represent this situation. Equation:______________________________________ How many square blocks will be in the 88 th figure? xy xy