1. 10-2 Graphing Functions Learn to represent linear functions using ordered pairs and graphs.

2. 10-2 Graphing Functions Vocabulary linear equation

3. 10-2 Graphing Functions 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. 184(4) + 24 144(3) + 23 104(2) + 22 64(1) + 21 y4x + 2x Write these solutions as ordered pairs. (x, y) ‏ (1, 6) ‏ (2, 10) ‏ (3, 14) ‏ (4, 18) ‏

4. 10-2 Graphing Functions Check It Out: 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. 173(5) + 25 143(4) + 24 113(3) + 23 83(2) + 22 y3x + 2x Write these solutions as ordered pairs. (x, y) ‏ (2, 8) ‏ (3, 11) ‏ (4, 14) ‏ (5, 17) ‏

5. 10-2 Graphing Functions 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.

6. 10-2 Graphing Functions 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.

7. 10-2 Graphing Functions Check It Out: 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.

8. 10-2 Graphing Functions 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.

9. 10-2 Graphing Functions 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

10. 10-2 Graphing Functions Check It Out: 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

11. 10-2 Graphing Functions Additional Example 4: Graphing Linear Functions Graph the function described by the equation. y = –x – 2 Make a function table. –3–(1) – 21 –2–(0) – 20 –1–(–1) – 2–1 y–x – 2x Write these solutions as ordered pairs. (x, y) ‏ (–1, –1) ‏ (0, –2) ‏ (1, –3) ‏

12. 10-2 Graphing Functions 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.

13. 10-2 Graphing Functions Check It Out: Example 4 Graph the function described by the equation. y = –x – 4 Make a function table. –5–(1) – 41 –4–(0) – 40 –3–(–1) – 4–1 y–x – 4x Write these solutions as ordered pairs. (x, y) ‏ (–1, –3) ‏ (0, –4) ‏ (1, –5) ‏

14. 10-2 Graphing Functions Check It Out: 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.