Alg II 2-3 and 2-4 Linear Functions


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Alg II 2-3 and 2-4 Linear Functions

  1. 1. Algebra II Chapter 2 Functions, Equations, and Graphs©Tentinger
  2. 2.  Essential Understanding: If you move from any point on a nonvertical line in the coordinate plane to any other point on the line, the ratio of the vertical change to the horizontal change is constant. The constant ratio is the slope of the line. The slopes of two lines in the same plane indicate how the lines are related. Objectives  Students will be able to graph linear equations  Students will be able to write equations of lines  Students will be able to write an equation of a line given its slope and a point on the line
  3. 3.  Algebra A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Functions 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.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. F-IF.9. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
  4. 4.  What is slope? The ratio of vertical change to horizontal change between two lines.
  5. 5.  Find the slope of the line that passes through the given points. (5, 4) and ( 8, 1) (2, 2) and (-2, -2) (9, 3) and (9, -4) Does it matter what point you choose to be first when using the slope formula?
  6. 6.  How many different types of slopes are there?
  7. 7.  What is a linear function? What determines if a line is linear? What does a solution to a linear equation represent? What is a y-intercept? What is an x-intercept? There are two ways to represent a linear equation, what are they?
  8. 8.  y = mx + b What does each letter represent? What is the equation of the line with m = 6 and y-intercept (0, 5)? Rewrite in slope-intercept form: 3x + 2y = 18 What is the graph of 4x – 7y = 14?
  9. 9.  y – y1 = m(x – x1), where (x1, y1) is a point What is an equation of the line through (7, -1) with slope -3? A line passes through (-5, 0) and (0, 7). What is an equation of the line in point-slope form?
  10. 10.  Ax + By = C, where A and B are real numbers and are not both zero What is an equation of the line y = 9.1x +3.6 in standard form? What is the equation of the line y = (2/5)x – 3?
  11. 11.  Slope Intercept Form  y = mx + b  Use when you know the slope and the y – intercept Point Slope Form  y – y1 = m(x – x1)  Use when you know the slope and a point or if you know two points Standard Form  Ax + By = C
  12. 12.  What are the intercepts of 2x – 4y = 8? Graph the equation. The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she knows that the paper will last about 80 days.  What graph represents this situation?  What is the equation of the line in standard form?  How many packs of a printer paper should the manager expect to have after 30 days?
  13. 13.  How do you know if two lines are parallel? Slopes are equal
  14. 14.  How do you know if two lines are perpendicular? Slopes are negative reciprocals (opposite re”flip”rocals) If you multiply the slopes together, it equals -1
  15. 15.  What is the equation of each line in slope- intercept form? The line parallel to 4x + 2y = 7 through (4, -2) The line perpendicular to y = (2/3)x – 1 through (0, 6)
  16. 16.  Pg. 78 # 9 – 39 (3’s), 47 - 49 Pg. 86 #3 – 42 (3’s) 26 problems