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Linear Functions: Identifying and Graphing

Learn to identify linear functions and write them in standard form. Understand how to find and graph the x-intercept and y-intercept. Practice comparing properties of linear functions.

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Linear Functions: Identifying and Graphing

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  1. Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. CCSS

  2. You analyzed relations and functions. • Identify linear relations and functions. • Write linear equations in standard form. Then/Now

  3. linear relation • nonlinear relation • linear equation • linear function • standard form • y-intercept • x-intercept Vocabulary

  4. Identify Linear Functions A.State whether g(x) = 2x – 5 is a linear function. Write yes or no. Explain. Answer: Example 1A

  5. Identify Linear Functions A.State whether g(x) = 2x – 5 is a linear function. Write yes or no. Explain. Answer: Yes; this is a linear function because it is in the form g(x) = mx + b; m = 2, b = –5. Example 1A

  6. Identify Linear Functions B.State whether p(x) = x3 + 2 is a linear function. Write yes or no. Explain. Answer: Example 1B

  7. Identify Linear Functions B.State whether p(x) = x3 + 2 is a linear function. Write yes or no. Explain. Answer: No; this is not a linear function because x has an exponent other than 1. Example 1B

  8. A. State whether h(x) = 3x – 2 is a linear function. Explain. A. yes; m = –2, b = 3 B. yes; m = 3, b = –2 C. No; x has an exponent other than 1. D. No; there is no slope. Example 1A

  9. A. State whether h(x) = 3x – 2 is a linear function. Explain. A. yes; m = –2, b = 3 B. yes; m = 3, b = –2 C. No; x has an exponent other than 1. D. No; there is no slope. Example 1A

  10. B. State whether f(x) = x2 – 4 is a linear function. Explain. A. yes; m = 1, b = –4 B. yes; m = –4, b = 1 C. No; two variables are multiplied together. D. No; x has an exponent other than 1. Example 1B

  11. B. State whether f(x) = x2 – 4 is a linear function. Explain. A. yes; m = 1, b = –4 B. yes; m = –4, b = 1 C. No; two variables are multiplied together. D. No; x has an exponent other than 1. Example 1B

  12. C. State whether g(x, y) = 3xy is a linear function. Explain. A. yes; m = 3, b = 1 B. yes; m = 3, b = 0 C. No; two variables are multiplied together. D. No; x has an exponent other than 1. Example 1C

  13. C. State whether g(x, y) = 3xy is a linear function. Explain. A. yes; m = 3, b = 1 B. yes; m = 3, b = 0 C. No; two variables are multiplied together. D. No; x has an exponent other than 1. Example 1C

  14. A. 50 miles B. 5 miles C. 2 miles D. 0.5 miles Example 2A

  15. A. 50 miles B. 5 miles C. 2 miles D. 0.5 miles Example 2A

  16. Concept

  17. Standard Form Write y = 3x – 9 in standard form. Identify A, B, and C. y = 3x – 9 Original equation –3x + y = –9 Subtract 3x from each side. 3x – y = 9 Multiply each side by –1 so that A≥ 0. Answer: Example 3

  18. Standard Form Write y = 3x – 9 in standard form. Identify A, B, and C. y = 3x – 9 Original equation –3x + y = –9 Subtract 3x from each side. 3x – y = 9 Multiply each side by –1 so that A≥ 0. Answer: 3x – y = 9; A = 3, B = –1, and C = 9 Example 3

  19. Write y = –2x + 5 in standard form. A.y = –2x + 5 B. –5 = –2x + y C. 2x+ y = 5 D. –2x– 5 = –y Example 3

  20. Write y = –2x + 5 in standard form. A.y = –2x + 5 B. –5 = –2x + y C. 2x+ y = 5 D. –2x– 5 = –y Example 3

  21. Use Intercepts to Graph a Line Find the x-intercept and the y-intercept of the graph of –2x + y – 4 = 0. Then graph the equation. The x-intercept is the value of x when y = 0. –2x + y– 4 = 0 Original equation –2x + 0– 4 = 0 Substitute 0 for y. –2x = 4 Add 4 to each side. x = –2 Divide each side by –2. The x-intercept is –2. The graph crosses the x-axis at (–2, 0). Example 4

  22. Use Intercepts to Graph a Line Likewise, the y-intercept is the value of y when x = 0. –2x + y – 4 = 0 Original equation –2(0) + y – 4 = 0 Substitute 0 for x. y = 4 Add 4 to each side. The y-intercept is 4. The graph crosses the y-axis at (0, 4). Example 4

  23. Use Intercepts to Graph a Line Use the ordered pairs to graph this equation. Answer: Example 4

  24. Use Intercepts to Graph a Line Use the ordered pairs to graph this equation. Answer: The x-intercept is –2, and the y-intercept is 4. Example 4

  25. What are the x-intercept and the y-intercept of the graph of 3x – y + 6 = 0? A.x-intercept = –2y-intercept = 6 B.x-intercept = 6y-intercept = –2 C.x-intercept = 2y-intercept = –6 D.x-intercept = –6y-intercept = 2 Example 4

  26. What are the x-intercept and the y-intercept of the graph of 3x – y + 6 = 0? A.x-intercept = –2y-intercept = 6 B.x-intercept = 6y-intercept = –2 C.x-intercept = 2y-intercept = –6 D.x-intercept = –6y-intercept = 2 Example 4

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