1. Check 12-1 HW

2. Course 1 12-2 Graphing Functions 6 th Grade Math HOMEWORK Page 608 #7-20

3. Course 1 12-1 Tables and Functions Our Learning Goal Students will understand functions by creating tables and graphing translations.

4. Course 1 12-1 Tables and Functions Students will understand functions by creating tables and graphing translations. Learn to use data in a table to write an equation for a function and to use the equation to find a missing value. Learn to represent linear functions using ordered pairs and graphs. Learn to use translations to change the positions of figures on a coordinate plane. Learn to use reflections to change the positions of figures on a coordinate plane. Learn to use rotations to change positions of figures on a coordinate plane. Learn to visualize and show the results of stretching or shrinking a figure.

5. Today’s Learning Goal Assignment Learn to represent linear functions using ordered pairs and graphs. Course 1 12-2 Graphing Functions

6. 12-2 Graphing Functions Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

7. Warm Up Write an equation for each function. Tell what each variable you use represents. 1. The length of a wall is 4 ft more than three times the height. 2. The number of trading cards is 3 less than the number of buttons. l = 3h + 4, where l is length and h is height. c = b – 3, where c is the number of cards and b is the number of buttons. Course 1 12-2 Graphing Functions

8. Problem of the Day Steve saved $1.50 each week. How many weeks did it take him to save enough to buy a $45 skateboard? 30 Course 1 12-2 Graphing Functions

9. Vocabulary linear equation Insert Lesson Title Here Course 1 12-2 Graphing Functions

10. Additional Example 1: Finding Solutions of Equations with Two Variables Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x =1, 2, 3, 4. Make a function table by using the given values for x to find values for y. x4x + 2y 14(1) + 26 24(2) + 210 34(3) + 214 44(4) + 218 Write these solutions as ordered pairs. (x, y) (1, 6) (2, 10) (3, 14) (4, 18) Course 1 12-2 Graphing Functions

11. Try This: Example 1 Use the given x-values to write solutions of the equation y = 3x + 2 as ordered pairs. x = 2, 3, 4, 5. Make a function table by using the given values for x to find values for y. x3x + 2y 23(2) + 28 33(3) + 211 43(4) + 214 53(5) + 217 Write these solutions as ordered pairs. (x, y) (2, 8) (3, 11) (4, 14) (5, 17) Course 1 12-2 Graphing Functions

12. Insert Lesson Title Here Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement. Course 1 12-2 Graphing Functions

13. Additional Example 2: Checking Solutions of Equations with Two Variables Determine whether the ordered pair is a solution to the given equation. (3, 21); y = 7x y = 7x Write the equation. 21 = 7(3) ? 21 = 21 ? Substitute 3 for x and 21 for y. So (3, 21) is a solution to y = 7x. Course 1 12-2 Graphing Functions

14. Try This: Example 2 Determine whether the ordered pair is a solution to the given equation. (4, 20); y = 5x y = 5x Write the equation. 20 = 5(4) ? 20 = 20 ? Substitute 4 for x and 20 for y. So (4, 20) is a solution to y = 5x. Course 1 12-2 Graphing Functions

15. Insert Lesson Title Here You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs of some functions, they form a straight line. The equations that express these functions are called linear equations. Course 1 12-2 Graphing Functions

16. Insert Lesson Title Here Additional Example 3: Reading Solutions on Graphs Use the graph of the linear function to find the value of y for the given value of x. x = 4 When x = 4, y = 2. Start at the origin and move 4 units right. Move up until you reach the graph. Move left to find the y-value on the y-axis. The ordered pair is (4, 2). x y -4 -2 0 2 4 4 -2 -4 2 Course 1 12-2 Graphing Functions

17. Insert Lesson Title Here Try This: Example 3 Use the graph of the linear function to find the value of y for the given value of x. x = 2 When x = 2, y = 4. Start at the origin and move 2 units right. Move up until you reach the graph. Move left to find the y-value on the y-axis. The ordered pair is (2, 4). x y -4 -2 0 2 4 4 -2 -4 2 Course 1 12-2 Graphing Functions

18. Additional Example 4: Graphing Linear Functions Graph the function described by the equation. y = –x – 2 Make a function table. x–x – 2y –1–(–1) – 2–1 0–(0) – 2–2 1–(1) – 2–3 Write these solutions as ordered pairs. (x, y) (–1, –1) (0, –2) (1, –3) Course 1 12-2 Graphing Functions

19. Insert Lesson Title Here Additional Example 4 Continued x y Graph the ordered pairs on a coordinate plane. -5 -4 -3 -2 -1 0 1 2 3 4 5 5 4 3 2 1 -5 -4 -3 -2 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y. Course 1 12-2 Graphing Functions

20. Try This: Example 4 Graph the function described by the equation. y = –x – 4 Make a function table. x–x – 4y –1–(– 1) – 4–3 0–(0) – 4–4 1–(1) – 4–5 Write these solutions as ordered pairs. (x, y) (–1, –3) (0, –4) (1, –5) Course 1 12-2 Graphing Functions

21. Insert Lesson Title Here Try This: Example 4 x y Graph the ordered pairs on a coordinate plane. -5 -4 -3 -2 -1 0 1 2 3 4 5 5 4 3 2 1 -5 -4 -3 -2 Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y. Course 1 12-2 Graphing Functions

22. Lesson Quiz 1. Use the given x-values to write solutions as ordered pairs to the equation y = –3x + 1 for x = 0, 1, 2, and 3. 2. Determine whether (4, –2) is a solution to the equation y = –5x + 3. 3. Graph the function described by the equation y = –x + 3. No, –2 ≠ –5(4) + 3 (0, 1), (1, –2), (2, –5), (3, –8) Insert Lesson Title Here Course 1 12-2 Graphing Functions