1. Chapter 4 Graphing Linear Equations and Functions  Lesson 4.1  Plot points in a coordinate plane

2. Point A is 3 units to the left of the origin and 4 units up. So, the x- coordinate is – 3, and the y- coordinate is 4. The coordinates are (– 3, 4). a.a. SOLUTION EXAMPLE 1 Name points in a coordinate plane Give the coordinates of the point. A a.a. B b.b.

3. b.b. Point B is 2 units to the right of the origin and 3 units down. So, the x- coordinate is 2, and the y- coordinate is – 3. The coordinates are (2, – 3). EXAMPLE 1 Name points in a coordinate plane

4. GUIDED PRACTICE for Example 1 1. Use the coordinate plane in Example 1 to give the coordinates of points C, D, and E. Point C is 2 units up from the origin. So, the x- coordinate is 0 and the y- coordinate is 2. The coordinates are (0, 2). C.C. SOLUTION

5. GUIDED PRACTICE for Example 1 D.D. Point D is 3 units to the right of the origin and 1 units up. So, the x- coordinate is 3, and the y- coordinate is 1. The coordinates are (3, 1). E.E. Point E is 2 units to the left of the origin and 3 units down. So, the x- coordinate is – 2, and the y- coordinate is – 3. The coordinates are (– 2, – 3).

6. GUIDED PRACTICE for Example 1 y -coordinate of any point on the x -axis is 0 2. What is the y -coordinate of any point on the x -axis ? SOLUTION

7. Plot the point in a coordinate plane. Describe the location of the point. EXAMPLE 2 Plot points in a coordinate plane Begin at the origin. First move 4 units to the left, then 4 units up. Point A is in Quadrant II. a.a. Begin at the origin. First move 3 units to the right, then 2 units down. Point B is in Quadrant IV. b.b. A(– 4, 4) a.a. B(3, –2) b.b. C(0, – 4) c.c.

8. Begin at the origin and move 4 units own. Point C is on the y- axis. c.c. EXAMPLE 2 Plot points in a coordinate plane

9. Make a table by substituting the domain values into the function. STEP 1 SOLUTION Graph the function y = 2x – 1 with domain – 2, – 1, 0, 1, and 2. Then identify the range of the function. EXAMPLE 3 Graph a function

10. STEP 2 List the ordered pairs: (– 2, – 5),(– 1, – 3), (0, – 1), (1, 1), (2, 3). Then graph the function. EXAMPLE 3 Graph a function

11. STEP 3 Identify the range. The range consists of the y -values from the table: – 5, – 3, – 1, 1, and 3. EXAMPLE 3 Graph a function

12. GUIDED PRACTICE for Examples 2 and 3 Plot the point in a coordinate plane. Describe the location of the point. 3. A(2, 5) SOLUTION Begin at the origin. First move 2 units to the right, then 5 units up. Point A is in Quadrant I.

13. GUIDED PRACTICE for Examples 2 and 3 SOLUTION 4. B(–1, 0) Begin at the origin and move 1 units to the left. Point B is on x -axis. 5. C(– 2, –1) SOLUTION Begin at the origin. First move 2 units to the left, then 1 units down. Point C is in Quadrant III.

14. GUIDED PRACTICE for Examples 2 and 3 SOLUTION Begin at the origin. First move 5 units to the left and then 3 units up. Point D is in Quadrant II. 6. D(–5, 3)

15. GUIDED PRACTICE for Examples 2 and 3 7. Graph the function y = – x + 2 with domain – 6, –3, 0, 3, and 6. Then identify the range of the function. 1 3 STEP 1 Make a table by substituting the domain values into the function.

16. GUIDED PRACTICE for Examples 2 and 3 y = – (6) + 2 = 06 y = – (3) + 2 = 13 y = – (0) + 2 = 20 y = – (– 3) + 2 = 3– 3 y = – (– 6) + 2 = 4– 6 y = – x + 2x 1 3 1 3 1 3 1 3 1 3 1 3

17. GUIDED PRACTICE for Examples 2 and 3 STEP 2 List the ordered pairs: (– 6, 4),(– 3, 3), (0, 2), (3, 1), (6,0). Then graph the function. STEP 3 Identify the range. The range consists of the y -values from the table: 0, 1, 2, 3 and 4.

18. Graph a function represented by a table EXAMPLE 4 VOTING In 1920 the ratification of the 19 th amendment to the United States Constitution gave women the right to vote. The table shows the number (to the nearest million) of votes cast in presidential elections both before and since women were able to vote.

19. Graph a function represented by a table EXAMPLE 4 Years before or since 1920 – 12– 8– 404812 Votes (millions) 15 1927293740 Explain how you know that the table represents a function. a.a. Graph the function represented by the table. b.b. Describe any trend in the number of votes cast. c.c.

20. Graph a function represented by a table EXAMPLE 4 SOLUTION The table represents a function because each input has exactly one output. a.a. To graph the function, let x be the number of years before or since 1920. Let y be the number of votes cast (in millions). b.b. The graph of the function is shown.

21. Graph a function represented by a table EXAMPLE 4 SOLUTION In the three election years before 1920, the number of votes cast was less than 20 million. In 1920, the number of votes cast was greater than 20 million. The number of votes cast continued to increase in the three election years since 1920. c.c.

22. GUIDED PRACTICE for Example 4 8. The presidential election in 1972 was the first election in which 18 -year-olds were allowed to vote. The table shows the number (to the nearest million) of votes cast in presidential elections both before and since 1972. VOTING Years before or since 1972 – 12– 8– 404812 Votes (millions) 69717378828793

23. GUIDED PRACTICE for Example 4 a. Explain how you know the graph represents a function. SOLUTION The table represents a function because each input has exactly one output.

24. GUIDED PRACTICE for Example 4 To graph the function, let x be the number of years before or since 1972. Let y be the number of votes cast. b.b. b. Graph the function represented by the table. SOLUTION

25. GUIDED PRACTICE for Example 4 Before 1972, the number of votes cast increased by 2 million every 4 years. In 1972, the number increased by 5 million and continued to increase by more than 2 million every four years since 1972. c.c. c. Describe any trend in the number of votes cast. SOLUTION