1. Modified LTF activity

2.  Graph y = 2x. Plot at least 5 points

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.  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.  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.  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.  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.  Graph y = 2x. Plot at least 5 points

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.  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.  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.  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.  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.  How do the equations from #1 and #2 differ?

15.  How do the equations from #1 and #2 differ?
 How does this difference indicate the direction
of the horizontal translation?

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.  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. 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.  Graph y = ¼ x. Plot at least 4 points.

20.  Graph y = ¼ x. Plot at least 4 points.
 Translate the line to the right 2 units and up 3
units.

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.  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.  Graph y = 3x. Plot at least 4 points.

24.  Graph y = 3x. Plot at least 4 points.
 Translate the line 1 unit left and 3 units down.

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.  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.  How does the equation tell us the horizontal
translation? The vertical translation?

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. 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.  This equation that shows the translation is
written as y – y1 = m(x – x1) and is called
POINT-SLOPE FORM. Justify this name.

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. Slope Point Equation
5 (3, 5)
7 (-5, 9)
-2 (2, -4)
1 (-3, -3)
-1/2 (0, 4)