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Master Linear Functions: Ordered Pairs & Graphs

Learn to represent linear functions using ordered pairs and graphs. Create function tables, check solutions, and graph equations on a coordinate plane. Understand linear equations and solve problems step-by-step.

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Master Linear Functions: Ordered Pairs & Graphs

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  1. Learn to represent linear functions using ordered pairs and graphs.

  2. Vocabulary linear equation

  3. Make a function table by using the given values for x to find values for y. Write these solutions as ordered pairs. x 4x + 2 y 1 4(1) + 2 6 2 4(2) + 2 10 3 4(3) + 2 14 4 4(4) + 2 18 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. (x, y)‏ (1, 6)‏ (2, 10)‏ (3, 14)‏ (4, 18)‏

  4. Make a function table by using the given values for x to find values for y. Write these solutions as ordered pairs. x 3x + 2 y 2 3(2) + 2 8 3 3(3) + 2 11 4 3(4) + 2 14 5 3(5) + 2 17 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. (x, y)‏ (2, 8)‏ (3, 11)‏ (4, 14)‏ (5, 17)‏

  5. 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. Write the equation. ? 21= 7(3)‏ Substitute 3 for x and 21 for y. ? 21= 21 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  So (3, 21) is a solution to y = 7x.

  7. Write the equation. ? 20= 5(4)‏ Substitute 4 for x and 20 for y. ? 20= 20 Check It Out: Example 2 Determine whether the ordered pair is a solution to the given equation. (4, 20); y = 5x y = 5x  So (4, 20) is a solution to y = 5x.

  8. 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. Start at the origin and move 4 units right. y Move up until you reach the graph. Move left to find the y-value on the y-axis. x 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 4 2 -4 -2 0 2 4 -2 When x = 4, y = 2. The ordered pair is (4, 2). -4

  10. Start at the origin and move 2 units right. y Move up until you reach the graph. Move left to find the y-value on the y-axis. x 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 4 2 -4 -2 0 2 4 -2 When x = 2, y = 4. The ordered pair is (2, 4). -4

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

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

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

  14. Graph the ordered pairs on a coordinate plane. y Draw a line through the points to represent all the values of x you could have chosen and the corresponding values of y. x Check It Out: Example 4 Continued 5 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5

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