# Understanding slope and intercepts

415 Topic 10: Understanding slope and intercepts Lesson 4: Identifying Intercepts LESSON 4: OPENER Use the graph to answer the following questions. 1. Identify the point on the line that represents the y-intercept. What are the coordinates of this point? 2. Identify the point on the line that represents the x-intercept. What are the coordinates of this point? 3. Use the x- and y-intercepts to calculate the slope of the line. LESSON 4: PRE-EVALUATION I can identify the y-intercept f of a line Not Proficient Approaching Proficiency Proficient Mastery Proficient Mastery Approaching Proficiency Proficient Mastery Approaching Proficiency Proficient Mastery I can identify the y-intercept from an equation of a line Not Proficient Approaching Proficiency I can identify the y-intercept from a table Not Proficient I can calculate slope Not Proficient Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc. 416 Topic 10: Understanding slope and intercepts LESSON 4: CORE ACTIVITY The y-intercept is when x = 0 or when the line crosses the y-axis. Find the y-intercept for the following linear relationships. Extra credit: Find the slope afterwards! 7) y = -5x + 3 8) y = 2x – 5 9) 2x + 3y = 6 10) y = -7x Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc. 417 Topic 10: Understanding slope and intercepts 11) 12) 13) 14) LESSON 4: POST-EVALUATION I can identify the y-intercept f of a line Not Proficient Approaching Proficiency Proficient Mastery Proficient Mastery Approaching Proficiency Proficient Mastery Approaching Proficiency Proficient Mastery I can identify the y-intercept from an equation of a line Not Proficient Approaching Proficiency I can identify the y-intercept from a table Not Proficient I can calculate slope Not Proficient Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc. 415 Topic 10: Understanding slope and intercepts Lesson 2: Connecting slope and rate of change through multiple representations LESSON 2: OPENER Shawna earns $10 each week helping her grandmother. She decides to save her money in the bank. Complete the table representing the data from Shawna’s situation. Then indicate the first differences for “Time in weeks” and “Amount saved.” Time in weeks (t) Process Amount saved (a) 1 2 3 4 5 6 t LESSON 1: GOALS PRE-EVALUATION AND POST-EVALUATION I can determine if a function is linear by using first difference Not Proficient Approaching Proficiency Proficient Mastery I can explain the meaning for x- and y-intercepts for the situation being modeled Not Proficient Approaching Proficiency Proficient Mastery I can use the connection between rate of change and slope to analyze and graph linear functions Not Proficient Approaching Proficiency Proficient Mastery I am confident in using tables, graphs and functions rules for linear relationships Not Proficient Approaching Proficiency Proficient Mastery Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc. 416 Topic 10: Understanding slope and intercepts LESSON 2: CORE ACTIVITY Slope equation as often written Δy y2 − y1 “#$%&’ (% ) Slope = = = Δx x2 − x1 “#$%&’ (% * ! Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc. 417 Topic 10: Understanding slope and intercepts Find the slope of the line through each pair of points. 7) (16, 1), (17, 7) 8) (−16, 7), (−15, 17) 9) (2, 8), (7, 8) 10) (−11, 15), (−11, 6) Find the slope of the line for each table. 11) 13) 12) 14) Copyright © 2017 Charles A. Dana Center at the University of Texas at Austin, Learning Sciences Research Institute at the University of Illinois at Chicago, Agile Mind, Inc. End of Unit 3 Study Guide 1. Define the following terms: 2. Describe the process you use to find the rate from a table or two-points on a graph? a.) Constant Rate of Change: b.) Proportional Relationship: c.) Constant of Proportionality: 3. 4. Time (minutes) 1 Depth of Water (inches) 12 x y 0 8 2 15 1 10 3 18 2 12 4 21 3 14 5 24 4 16 a.) Does the date represent a proportional relationship? b.) What is the rate of change? SHOW ALL YOUR WORK. a.) Describe why this data represents a constant rate of change. 5. 6. x y 0 3 2 11 4 19 6 27 8 35 a.) What is the rate of change? SHOW ALL YOUR WORK. 7. Time (minutes) 0 Amount of water (gallons) 75 5 125 15 175 25 225 35 275 a.) What is the rate of change? SHOW ALL YOUR WORK. 8. a.) What is the rate of change. a.) What is the rate of change. Graph Segment A:_________________ Graph Segment B:_________________ Graph Segment C:_________________ Graph Segment D: ________________

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