Linear functions

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Linear functions

  1. 1. 1Sep 23­03:21 p.m.Linear functionsDuring this lesson we will  :• Explore the equation of a straight line.• Discover algebraic relations between pairs of    parallel and perpendicular lines.• Explore the absolute value function and its    properties.• Recognise and draw piecewise linear functions.
  2. 2. 2Sep 23­03:21 p.m.Distance between two pointsAB
  3. 3. 3Sep 23­03:21 p.m.The Midpoint formula:ABMx1 x2
  4. 4. 4Sep 23­03:21 p.m.Linear functionsThe graph is a straight line.
  5. 5. 5Sep 23­03:21 p.m.Gradient of a lineThe gradient of a line is a measure of its steepnessIfandpositive gradient negative gradient
  6. 6. 6Sep 23­03:21 p.m.horizontal lines have a gradient of 0 (zero)vertical lines have an undefined gradientparallel lines have equal gradientsthe gradients of perpendicular lines arenegative reciprocalsif the gradients are m1 and m2 then:or
  7. 7. 7Sep 23­03:21 p.m.Equations of linesThe equation of a line is an equation which states the connectionbetwen the x and y values for every point on the line.All vertical lines have equations of the form x = a , ( a is a constant)All horizontal lines have equations of the form y = c , ( c is a constant)slope-intercept form or explicit formgradienty-interceptgeneral form or implicit form(not a function)
  8. 8. 8Sep 23­03:21 p.m.Write down the gradient and y-intercept of these straightlines:y = 5x ­ 22y = 1 ­ 6 x3x + 2y ­ 8 = 0
  9. 9. 9Sep 23­03:21 p.m.Sketch the graphs of these equations:y = 2 x ­ 1  3y + 2x  ­3 = 0 2y ­ x + 1 = 0 
  10. 10. 10Sep 23­03:21 p.m.Write down the equation of the straight line which passesthrough the points A (2,5) and B (6,17).
  11. 11. 11Sep 23­03:21 p.m.Find the explicit and implicit equations of the linethrough (-1,3) with a slope of 5.
  12. 12. 12Sep 23­03:21 p.m.Are L1 with equation 2x ­ y + 2=0 and L2 with equationx + 4y ­ 1 = 0 perpendicular lines?
  13. 13. 13Sep 23­03:21 p.m.Find the equation of the line through (1,-5) and (5,-2).Express the equation in the form Ax+By + C = 0, with A, B and Cinteger numbers.
  14. 14. 14Sep 23­03:21 p.m.Interceptsx­intercepty­interceptxyThe x-intercept is found by letting y =0.The y-intercept is found by letting x=0.
  15. 15. 15Sep 23­03:21 p.m.For the line with equation 2x - 3y =12, find axis intercepts.
  16. 16. 16Sep 23­03:21 p.m.Find the point of intersection of the lines :3x+4y=29 and 2x ­ 5y=43x+4y=292x ­ 5y=4
  17. 17. 17Sep 23­03:21 p.m.At the end of the lesson:Reproduce exactly this drawing on your GDC.
  18. 18. 18Sep 23­03:21 p.m.At the end of the lesson:Reproduce exactly this drawing on your GDC.
  19. 19. 19Sep 23­03:21 p.m.Can you give a formula for the followinggraph?
  20. 20. 20Sep 23­03:21 p.m. Piecewise linear functionsDraw the graph of:
  21. 21. 21Sep 23­03:21 p.m.Absolute valueExamples:1 ­ |­6| =|π­3|= |2π­ 7|=
  22. 22. 22Sep 23­03:21 p.m.Equations:
  23. 23. 23Sep 23­03:21 p.m.|x|≤3|x ­ 1 | ≤ 4In general: | x | ≤ a  ⇒  ­a  ≤  x ≤ a­a a0
  24. 24. 24Sep 23­03:21 p.m.|x|>5|x ­ 2 | ≥ 4In general: | x | >a  ⇒ x  < ­a   or   x> a­a a0
  25. 25. 25Sep 23­03:21 p.m.Absolute value function (Modulus)Sketch the graph of f(x).
  26. 26. 26Sep 23­03:21 p.m.
  27. 27. 27Sep 23­03:21 p.m.With calculator: Menu graphOPTNNum (F5)Abs (X)CasioTI-84 Y=MATH > 1 (X )
  28. 28. AttachmentsY11    Linear functions 2010.odt

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