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Linear Functions Identification and Graphing

Learn how to identify linear functions, write equations in standard form, and graph linear equations using intercepts. Practice analyzing relations and functions to interpret key features of graphs and tables. Compare properties of different functions represented in various ways.

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Linear Functions Identification 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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