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Unit 3 Linear Functions and Patterns

Unit 3 Linear Functions and Patterns . Big Idea: Linear Functions and Patterns Objective: The student will learn how to interpret graphs Common Core Mathematics Standard 2. Interpret graphs. Read GET READY for the Lesson, p. 53 What does the point B on the graph represent?

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Unit 3 Linear Functions and Patterns

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  1. Unit 3 Linear Functions and Patterns

  2. Big Idea: Linear Functions and Patterns Objective: The student will learn how to interpret graphs Common Core Mathematics Standard 2

  3. Interpret graphs Read GET READY for the Lesson, p. 53 What does the point B on the graph represent? About what percent of normal blood flow occurs two days after the injury? On what does the percent of blood flow depend?

  4. Vocabulary Interpret graphs function A relation between input and output. In a function, the output depends on the input.

  5. Vocabulary Interpret graphs Coordinate system Used to graph a function Formed by the intersection of two number lines, the horizontal axis and vertical axis

  6. Vocabulary Interpret graphs Coordinate system Used to graph a function Formed by the intersection of two number lines, the horizontal axis and vertical axis

  7. VocabularyInterpret graphs Vertical axis : y-axis Ordered pair (x, y) (3, 2) Origin : (0, 0) Horizontal axis : x-axis

  8. I / WE / YOU DO Interpret graphs I / WE DO - Example 1, p. 53 YOU DO -√ Your Progress, p. 53 #1

  9. Vocabulary Interpret graphs In the example the blood flow depends on the number of days since the injury. Independent variable Dependent variable The number of days since the injury The percent of normal blood flow

  10. I / WE / YOU DO Interpret graphs I DO - Example 2, p. 54 WE DO - √ Your Progress - p.54 #2A YOU DO - √ Your Progress - p.54 #2B

  11. I / WE / YOU DO Interpret graphs I / WE DO -Example 3, p. 54 YOU DO -√ Your Progress - p.54 #3

  12. I / WE / YOU DO Interpret graphs I / WE DO -Example 4, p. 55 YOU DO -√ Your Progress - p.55 #4

  13. Practice Interpret graphs Demonstration of learning – p. 56 # 1 - 7 p. 56-58 # 10 - 21

  14. Big Idea: Linear Functions and Patterns Objective: The student will learn how to graph linear equations using x and y intercepts Common Core Mathematics Standard 2

  15. Graph using intercepts Read GET READY for the Lesson, p. 155 If a person consumes an average of 2000 calories per day, how many grams of fat should the person consume? How can you use the graph to answer the question?

  16. Vocabulary Graph using intercepts Linear equation Standard form of a linear equation The equation of a straight line

  17. I / WE / YOU DO Graph using intercepts I DO - Example 1, p. 155 WE DO -√ Your Progress - p. 156 #1A YOU DO -√ Your Progress - p. 156 #1B

  18. Vocabulary Graph using intercepts X-intercept y-intercept The x-coordinate of the point where the graph of an equation crosses the x-axis The y-coordinate of the point where the graph of an equation crosses the y-axis.

  19. VocabularyGraph using intercepts y-intercept : (0, y) (0, 4) x-intercept : (x, 0) (3, 0)

  20. I / WE / YOU DO Graph using intercepts IDO -Example 2, p. 156 WE DO -√ Your Progress - p. 156 #2A YOU DO -√ Your Progress - p. 156 #2B

  21. I / WE / YOU DO Graph using intercepts I / WE DO -Example 3, p. 157 YOU DO -√ Your Progress - p. 157 #3

  22. I / WE / YOU DO Graph using intercepts I DO -Example 4, p. 157 WE DO -√ Your Progress - p. 157 #4A YOU DO -√ Your Progress - p. 157 #4B

  23. I / WE / YOU DO Graph using intercepts I / WE DO -Example 5, p. 158 YOU DO -√ Your Progress - p. 158 #5

  24. Practice Graph using intercepts Demonstration of Learning – p. 158 # 1 - 11 p. 159-160 • Identify linear equations and write in standard form #12 -17 • Determine intercepts of each function #18 - 23 • Graph a linear equation using a table or intercepts #24 – 32 • Applications #33 – 38; 53 - 55

  25. Big Idea: Linear Functions and Patterns Objective: The student will learn how to solve problems using slope of a line. Common Core Mathematics Standard 2

  26. Slope of a line Read GET READY for the Lesson, p. 187 What is the slope of the roof if the rise is 10 and the run is 6? What might the rise and run be for a roof with a slope of 2?

  27. Vocabulary Slope of a line Rate of change rate of change = A ratio that describes, on average, how much one quantity changes with respect to another quantity

  28. Slope of a line The table on p.187 shows the distance a person has walked for various amounts of time rate of change = rate of change = rate of change = This means that the person walked 4 feet per second

  29. I / WE / YOU DO Slope of a line I DO -Example 1, p. 187 WE DO -√ Your Progress - p. 188 #1A YOU DO -√ Your Progress - p. 188 #1B

  30. I / WE / YOU DO Slope of a line I / WE DO -Example 2, p. 188 YOU DO -√ Your Progress - p. 188 #2

  31. Slope of a line (4, 5) slope = (1, 3)

  32. I / WE / YOU DO Positive slope of a line I DO - Example 3, p. 190 WE DO -√ Your Progress - p. 190 #3A YOU DO -√ Your Progress - p. 190 #3B

  33. I / WE / YOU DO Negative slope of a line I DO - Example 4, p. 190 WE DO -√ Your Progress - p. 190 #4A YOU DO -√ Your Progress - p. 190 #4B

  34. I / WE / YOU DO Zero slope of a line I DO - Example 5, p. 190 WE DO -√ Your Progress - p. 190 #5A YOU DO -√ Your Progress - p. 190 #5B

  35. I / WE / YOU DO Undefined slope of a line I DO - Example 6, p. 191 WE DO -√ Your Progress - p. 191 #6A YOU DO -√ Your Progress - p. 191 #6B

  36. I / WE / YOU DO Find coordinates given slope I DO - Example 7, p. 191 WE DO -√ Your Progress - p. 191 #7A YOU DO -√ Your Progress - p. 191 #7B

  37. Practice slope of a line Demonstration of Learning p.192 #1-13 p. 192-195 • Rate of change from a table or graph #14-19 • Slope of a line passing through 2 points #20 – 31; 36 - 39, 62 • Find coordinates given slope #32-35; 44-47 • Applications #48-57

  38. Big Idea: Linear Functions and Patterns Objective: The student will learn how to write and graph a linear function in slope-intercept form. Common Core Mathematics Standard 2

  39. Write & graph linear functions Read GET READY for the Lesson, p. 204 Does the line have a positive slope or negative slope? What do x and y represent in the equation? A checking plan offered by a bank includes a $10 monthly service fee and a $0.20 per check fee for accounts with an average daily balance of less than $2000. What equation describes this plan?

  40. Vocabulary Write & graph linear functions Slope intercept form of a linear equation where m is the slope and b is the y-intercept y = mx + b (0, b) O

  41. I / WE / YOU Write & graph linear functions I / WE DO Example 1, p. 204 YOU DO -√ Your Progress - p. 204 #1

  42. I / WE / YOU Write & graph linear functions I / WE DO Example 2, p. 205 YOU DO -√ Your Progress - p. 205 #2

  43. I / WE / YOU Write & graph linear functions I DO - Example 3, p. 205 WE DO -√ Your Progress - p. 205 #3A WE DO -√ Your Progress - p. 205 #3C YOU DO -√ Your Progress - p. 205 #3B YOU DO -√ Your Progress - p. 205 #3D

  44. Vocabulary Write & graph linear functions Starting point Rate of change The y- intercept of a linear equation that models real-world data. The slope of a linear equation that models real world data.

  45. I / WE / YOU Write & graph linear functions I / WE DO Example 4, p. 206 YOU DO -√ Your Progress - p. 206 #4

  46. Practice Write & graph linear functions p. 207 - 208 • Write a linear function given slope and y-intercept #11 – 17, 39 - 44 • Write a linear function given a graph #18 – 23 • Graph a linear function given an equation. #24 – 32 • Applications #33 -38

  47. Big Idea: Linear Functions and Patterns Objective: The student will learn how to write a linear function and use it to solve problems. Common Core Mathematics Standard 2

  48. Linear functions Read GET READY for the Lesson, p. 213 How do you know that the slope is 7000? A biologist is studying how fast a bacteria grows. The population of bacteria has an average growth of 200 bacteria per hour. Describe the graph that demonstrates the growth.

  49. I / WE / YOU Linear functions I / WE DO - Example 1, p. 213 YOU DO -√ Your Progress - p. 213 #1

  50. I / WE / YOU Linear functions I / WE DO - Example 2, p. 214 YOU DO -√ Your Progress - p.214 #2

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