1. Translations of Linear Functions
Define the two terms in your own words with regards to math:
Translation
Linear Function

2. Answers Define the two terms in your own words:
Translation – a slide of a figure where every point is moved the same direction and same distance
Linear Function – any function that graphs to a straight line

3. An example of four linear functions translated to a new position.

4. Translations of Linear Functions
COMMON CORE #8, #31a, #36
Basically, exploring the change from y = x to y = m(x – h) + k
IT WILL NOT BE EASY
GET YOUR GAME FACE ON!!!!!!!!!!!!!!

5. Translations of Linear Functions
Graph y = 2x
Translate the graph 4 units to the right by moving each point you plotted.
Write the equation of the translated line.
y = 2x - 8

6. Translations of Linear Functions
y = 2x – 8
(4) Factor the expression:
y = 2(x – 4)
(5) What are the coordinates of the translated point (0, 0)
(4, 0)

7. Translations of Linear Functions
y = 2x (0, 0)
y = 2(x – 4) (4, 0)
(6) Where does the amount of the translation appear in the factored form of the equation?
-4 which moves it right 4 units

8. Translations of Linear Functions
y = mx + b
y = 2x
y = m(x – h) + k
y = 2(x – 4) + k
What about k?
It is 0 in this case as we did not move up or down(y- axis)

9. Translations of Linear Functions
(7) Graph y = 2x
(8) Translate the graph 4 units to the left by moving each point you plotted.
(9) Write the equation of the translated line.
y = 2x + 8

10. Translations of Linear Functions
y = 2x + 8
(10) Factor the expression:
y = 2(x + 4)
(11) What are the coordinates of the translated point (0, 0)
(-4, 0)

11. Translations of Linear Functions
y = 2x (0, 0)
y = 2(x + 4) (-4, 0)
(12) Where does the amount of the translation appear in the factored form of the equation?
+4 which moves it left 4 units

12. Translations of Linear Functions
y = mx + b
y = 2x
y = m(x – h) + k
y = 2(x – (-4)) + k
y = 2(x + 4) + k
What about k?
It is 0 in this case as we did not move up or down(y- axis)

13. Translations of Linear Functions
YOUR TURN TO TRY
GRAPH
y = 3(x – 2)

14. Translations of Linear Functions
YOUR TURN TO TRY
GRAPH
y = 4(x + 2)