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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)