Alg2 lesson 2.2 and 2.3

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Alg2 lesson 2.2 and 2.3

  1. 1. Name the domain and range for the relation shown in each graph<br />D = {x | x is a real number}<br />D = {x | x is a real number}<br />R = {y | y ≥ 0}<br />R = {y | y ≥ -2}<br />Lesson 2 Contents<br />
  2. 2. In a linear equation, each term is either a constant or the product of a constant and (the first power of) a single variable.<br />Which of these represent linear functions?<br />linear<br />nonlinear<br />linear<br />nonlinear<br />Example 2-1a<br />
  3. 3. Slope-intercept form<br /> y = mx + b<br /> f(x) = mx + b<br />m is the slope of the line<br />b is the y-intercept<br />What are the slope and y-intercept of the line ?<br />Slope = 3<br />y-intercept = -9<br />Example 2-1d<br />
  4. 4. The graph of a linear equation is a line.<br />Graph the line <br />y-intercept = -9<br />Slope = 3<br />Slope = ΔyΔx<br />Example 2-1d<br />
  5. 5. Standardform Ax + By = C <br /><ul><li> A, B and C are integers (not fractions!)
  6. 6. A is positive
  7. 7. A and B are not both zero</li></ul>3x + 5y = -2 is in standard form<br />Example 2-1d<br />
  8. 8. Write the equation in standard form. Identify A, B, and C. <br />Ax + By = C<br />Simplified?<br />2 2 2<br />Example 2-3c<br />
  9. 9. Write the equation in standard form. Identify A, B, and C. <br />Ax + By = C<br />Simplified?<br />Example 2-3a<br />
  10. 10. Write the equation in standard form. Identify A, B, and C. <br />Ax + By = C<br />-3 (-3)<br />Simplified?<br />Example 2-3b<br />
  11. 11. Find the x- and y- intercepts of -2x + y – 4 = 0<br />x-intercept<br />-2x + 0 – 4 = 0<br />-2x – 4 = 0<br />-2x = 4<br />x = -2<br />The x-intercept is -2<br /> (-2, 0)<br />y-intercept<br />-2(0) + y – 4 = 0<br />0 + y – 4 = 0<br />y – 4 = 0<br />y = 4<br />The y-intercept is 4<br /> (0, 4)<br />Example 2-4b<br />
  12. 12. (0, 4)<br />(–2, 0)<br />Graph -2x + y – 4 = 0<br />x-intercept : –2<br />y-intercept: 4<br />Example 2-4c<br />
  13. 13. Slope<br /> m = vertical change Horizontal change<br /> m = ΔyΔx<br /> m = rise run<br />Any two points on a line can be used to determine its slope.<br />
  14. 14. Find the slope of a line passing through (-3,5) & (2,1)<br />
  15. 15. Classification of lines by slope<br />Positive slope<br />Zero slope<br />Negative slope<br />Undefined slope<br />
  16. 16. Graph x = 1<br />Graph y = 3<br />
  17. 17. Parallel lines have equal slopes.<br />Perpendicular lines have slopes that are opposite reciprocals.<br />
  18. 18. Graph the line that passes through (2, 1) that is parallel to the graph of 4x – 2y = 10<br />4x – 2y =10<br />-2y = -4x + 10 -2 -2 -2<br /> y = 2x – 5<br />m = 2 , b = -5<br />Parallel slope = 2<br />
  19. 19. Graph the line that passes through (2, 1) that is perpendicular to the graph of 4x – 2y = 10<br />4x – 2y =10<br />-2y = -4x + 10 -2 -2 -2<br /> y = 2x – 5<br />m = 2 , b = -5<br />Perpendicular slope = -1/2<br />

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