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Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
Alg2 lesson 2.2 and 2.3
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Alg2 lesson 2.2 and 2.3

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  • 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. 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. 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. 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. Standardform Ax + By = C <br /><ul><li> A, B and C are integers (not fractions!)
  • 6. A is positive
  • 7. A and B are not both zero</li></ul>3x + 5y = -2 is in standard form<br />Example 2-1d<br />
  • 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. Write the equation in standard form. Identify A, B, and C. <br />Ax + By = C<br />Simplified?<br />Example 2-3a<br />
  • 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. 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. (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. 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. Find the slope of a line passing through (-3,5) &amp; (2,1)<br />
  • 15. Classification of lines by slope<br />Positive slope<br />Zero slope<br />Negative slope<br />Undefined slope<br />
  • 16. Graph x = 1<br />Graph y = 3<br />
  • 17. Parallel lines have equal slopes.<br />Perpendicular lines have slopes that are opposite reciprocals.<br />
  • 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. 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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