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 righ...
 Graph y = 2x. Plot at least 5 points
 Translate the graph 4 units to the right by
moving each point 4 units to the righ...
 Graph y = 2x. Plot at least 5 points
 Translate the graph 4 units to the right by
moving each point 4 units to the righ...
 Graph y = 2x. Plot at least 5 points
 Translate the graph 4 units to the right by
moving each point 4 units to the righ...
 Graph y = 2x. Plot at least 5 points
 Translate the graph 4 units to the right by
moving each point 4 units to the righ...
 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....
 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....
 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....
 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 translat...
 How do the equations from #1 and #2 differ?
 How does this difference indicate the direction
of the horizontal translat...
 How do the equations from #1 and #2 differ?
 How does this difference indicate the direction
of the horizontal translat...
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 hori...
 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 hori...
 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 tra...
 Graph y = 3x. Plot at least 4 points.
 Translate the line 1 unit left and 3 units down.
 Write the equation of the tra...
 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 conf...
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 – y1 = m(x – x1) and is called
POINT-SLOPE FORM. Justify this n...
 This equation that shows the translation is
written as y – y1 = m(x – x1) and is called
POINT-SLOPE FORM. Justify this n...
Slope Point Equation
5 (3, 5)
7 (-5, 9)
-2 (2, -4)
1 (-3, -3)
-1/2 (0, 4)
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Translations of linear functions

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Translations of linear functions

  1. 1. Modified LTF activity
  2. 2.  Graph y = 2x. Plot at least 5 points
  3. 3.  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.
  4. 4.  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.
  5. 5.  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.
  6. 6.  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?
  7. 7.  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?
  8. 8.  Graph y = 2x. Plot at least 5 points
  9. 9.  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.
  10. 10.  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.
  11. 11.  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.
  12. 12.  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?
  13. 13.  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?
  14. 14.  How do the equations from #1 and #2 differ?
  15. 15.  How do the equations from #1 and #2 differ?  How does this difference indicate the direction of the horizontal translation?
  16. 16.  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.
  17. 17.  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?
  18. 18. 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)
  19. 19.  Graph y = ¼ x. Plot at least 4 points.
  20. 20.  Graph y = ¼ x. Plot at least 4 points.  Translate the line to the right 2 units and up 3 units.
  21. 21.  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.
  22. 22.  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?
  23. 23.  Graph y = 3x. Plot at least 4 points.
  24. 24.  Graph y = 3x. Plot at least 4 points.  Translate the line 1 unit left and 3 units down.
  25. 25.  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.
  26. 26.  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?
  27. 27.  How does the equation tell us the horizontal translation? The vertical translation?
  28. 28.  How does the equation tell us the horizontal translation? The vertical translation?  What do you think is the most confusing part of the equation?
  29. 29. 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)
  30. 30.  This equation that shows the translation is written as y – y1 = m(x – x1) and is called POINT-SLOPE FORM. Justify this name.
  31. 31.  This equation that shows the translation is written as y – y1 = m(x – x1) and is called POINT-SLOPE FORM. Justify this name.  What does the m stand for? What do x1 and y1 stand for?
  32. 32. Slope Point Equation 5 (3, 5) 7 (-5, 9) -2 (2, -4) 1 (-3, -3) -1/2 (0, 4)

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