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Translations of linear functions

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Translations of linear functions Translations of linear functions Presentation Transcript

  • Modified LTF activity
    • Graph y = 2x. Plot at least 5 points
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the right by moving each point 4 units to the right.
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the right by moving each point 4 units to the right.
    • Write the equation of the translated line in slope-intercept form.
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the right by moving each point 4 units to the right.
    • Write the equation of the translated line in slope-intercept form.
    • Factor out the common factor in the translated equation.
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the right by moving each point 4 units to the right.
    • Write the equation of the translated line in slope-intercept form.
    • Factor out the common factor in the translated equation.
    • What are the coordinates of the point to which the point (0,0) is translated?
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the right by moving each point 4 units to the right.
    • Write the equation of the translated line in slope-intercept form.
    • Factor out the common factor in the translated equation.
    • What are the coordinates of the point to which the point (0,0) is translated?
    • Where does the amount of translation appear in the factored form of the equation?
    • Graph y = 2x. Plot at least 5 points
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the left by moving each point 4 units to the left.
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the left by moving each point 4 units to the left.
    • Write the equation of the translated line in slope-intercept form.
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the left by moving each point 4 units to the left.
    • Write the equation of the translated line in slope-intercept form.
    • Factor out the common factor in the translated equation.
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the left by moving each point 4 units to the left.
    • Write the equation of the translated line in slope-intercept form.
    • Factor out the common factor in the translated equation.
    • What are the coordinates of the point to which the point (0,0) is translated?
    • Graph y = 2x. Plot at least 5 points
    • Translate the graph 4 units to the left by moving each point 4 units to the left.
    • Write the equation of the translated line in slope-intercept form.
    • Factor out the common factor in the translated equation.
    • What are the coordinates of the point to which the point (0,0) is translated?
    • Where does the amount of translation appear in the factored form of the equation?
    • How do the equations from #1 and #2 differ?
    • How do the equations from #1 and #2 differ?
    • How does this difference indicate the direction of the horizontal translation?
    • How do the equations from #1 and #2 differ?
    • How does this difference indicate the direction of the horizontal translation?
    • Explain why y = 2(x+4) and y = 2(x-(-4)) represent the same line.
    • How do the equations from #1 and #2 differ?
    • How does this difference indicate the direction of the horizontal translation?
    • Explain why y = 2(x+4) and y = 2(x-(-4)) represent the same line.
    • What is the significance of the common factor?
  • Equation Slope New (0,0) Translation y = 3(x - 2) y = 4(x + 2) y = 10(x - 3) y = ½(x + 3) y = ½(x - 5)
    • Graph y = ¼ x. Plot at least 4 points.
    • Graph y = ¼ x. Plot at least 4 points.
    • Translate the line to the right 2 units and up 3 units.
    • Graph y = ¼ x. Plot at least 4 points.
    • Translate the line to the right 2 units and up 3 units.
    • We know that the horizontal translation is an x movement and shows up at ¼ (x – 2). If the vertical translation is a y movement, what should we write next to y? Write the full equation.
    • Graph y = ¼ x. Plot at least 4 points.
    • Translate the line to the right 2 units and up 3 units.
    • We know that the horizontal translation is an x movement and shows up at ¼ (x – 2). If the vertical translation is a y movement, what should we write next to y? Write the full equation.
    • Is the point (2,3) on the graph? How does it show up in the equation?
    • Graph y = 3x. Plot at least 4 points.
    • Graph y = 3x. Plot at least 4 points.
    • Translate the line 1 unit left and 3 units down.
    • Graph y = 3x. Plot at least 4 points.
    • Translate the line 1 unit left and 3 units down.
    • Write the equation of the translated line.
    • Graph y = 3x. Plot at least 4 points.
    • Translate the line 1 unit left and 3 units down.
    • Write the equation of the translated line.
    • What is the slope of this line? What point do we know for sure is on the line?
    • How does the equation tell us the horizontal translation? The vertical translation?
    • How does the equation tell us the horizontal translation? The vertical translation?
    • What do you think is the most confusing part of the equation?
  • Equation Slope Point on Line Translation y – 3 = 4(x + 2) y + 4 = 2(x – 1) y + 5 = 3x y – 7 = x + 5 y = -2(x – 3)
    • This equation that shows the translation is written as y – y 1 = m(x – x 1 ) and is called POINT-SLOPE FORM. Justify this name.
    • This equation that shows the translation is written as y – y 1 = m(x – x 1 ) and is called POINT-SLOPE FORM. Justify this name.
    • What does the m stand for? What do x 1 and y 1 stand for?
  • Slope Point Equation 5 (3, 5) 7 (-5, 9) -2 (2, -4) 1 (-3, -3) -1/2 (0, 4)