stepsaContinue these sequences for the next three terms and continue the sequences backwards to the previous 3 terms:

7, 10, 13, 16, 19, …

15, 18, 21, 24, 27, …

1, -2, -5, -8, -11,  …

What do you notice?

The first two sequences  come from a multiplication table shifted up. Which multiplication table is it? What can you say about the third sequence?

How do the sequences relate to the red steps in the diagram?

How do these sequences relate to the lines A, B and C in the diagram? Which sequence relates to which line?

How does the sequence 3, 5, 7, 9, 11, … relate a multiplication table and to the blue steps in the diagram? How does it relate to the line D in the diagram?

Imagine you are climbing the red steps from the point (-3 , -5) to the point (3, 13). Now imagine you climb the same number of the blue steps from the point (-3, -5) to the point (3, 7). Which is the steeper climb? Why? How could you measure the steepness of the climb?

Match the following equations to the lines in the diagram.

E_1: y = 3x + 12 \\ E_2: y = 2x + 1 \\ E_3: y = -3x + 4 \\ E_4: y = 3x + 4

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