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Unit Summary 2 Class : Algebra 1 Unit 2: Linear Functions – Chapter 5 I. Big Ideas: Students will understand how to use linear functions to model real world phenomena and solve problems arising from those situations. Students will understand how to translate among verbal, tabular, graphical, and algebraic representations of functions. Students will understand how to describe how slope and y-intercept appear in different representations. Students will understand that a linear function has infinitely many solutions that form a line. II. Topics that will be covered: 1. Writing expressions for the nth term 2. Rate of change 3. Defining slope 4. Graphing the equation of a line 5. Horizontal and vertical lines 6. Writing the equation of a line 7. Converting between standard form and slope-intercept form 8. Using the slope-intercept form for the equation of a line 9. Parallel lines 10. Perpendicular lines 11. X and y intercepts 12. Line of best fit 13. Scatter plot 14. Solving linear equations 15. Domain, range, and functions 16. Collinear III. Essential Questions: How does a graph relate to the equation of a line? What does it mean to be a linear function? In what ways can a linear graph be used to interpret data and find solutions? How can we create and solve linear systems to model real world situations? How can I use graphs to describe relationships? What do intercept x and y intercepts mean? How do I know if a point is a solution to an equation? What does it mean to have a positive, negative, zero, or undefined slope? IV. Sample questions to answer by the end of the unit: Write an equation for each table of values. 1. x y -3 5 -2 11 -1 17 0 23 1 29 2 35 3 41 x y -3 30 -2 26 -1 22 0 18 1 14 2 10 3 6 2. 3. The table below shows the amount that a company charges for a raft rental for up to 10 hours. An initial deposit is included in the amounts shown. Write an equation for the function. Time (x) 2 Cost (y) 20 4 30 6 40 8 50 10 60 A) How much does the company charge per hour? B) What is the initial deposit fee? 4. Which point is on the graph of the equation 3x + 6y = 27? A. (0,9) B. (5,2) C. (1,-5) D. (-5,7) 5. An equation for the line that crosses the x-axis at x = -1 and y-axis at y = 3 is A. 3x + y = 3 B. 3x = y + 3 C. y = 3x + 3 D. y + 3x = -3 6. Which line represents a horizontal line? A. y = x B. y = -2 C. x = 0 D. y = 2x + 1 7. The Smiths bought a house in 1975 for $90,000. In 1987, they sold it for $174,000. Assume that the increase in value was constant over this period. Let t = 0 in 1975. Write an equation for the value V of the house at any time t. Determine its value in 1989. When was its value $126,000? What is the slope and what does it mean in the context of this problem? Convert from standard form to slope intercept. 8. 4x – 3y = 12 9. –2x + 4y = 16 10. –3x – y = 5 Write an equation of each line in slope-intercept form. 11. A line with a slope of –3 and y-intercept of 12. 12. A line passing through (5, 0) and with y-intercept of 7. 13. A line containing the points (1, 5) and (2, 9). 14. A line passing through the origin and parallel to y = 5X + 9. Write an equation for the line that contains the point (2, 5) and is: 15. parallel to y = 2x – 1 16. perpendicular to y = 2x – 1 Graph the following two equations on the same coordinate grid. 17. y = 3/4x + 3 18. y = -2X – 3