Let vector $\displaystyle m = [2, -1]$ and vector $\displaystyle b = [0, 5]$

a) Determine the components of each vector in this list:

$\displaystyle b + 3m = [6, 2]$

$\displaystyle b + 2m = [4, 3]$

$\displaystyle b + m = [2, 4]$

$\displaystyle b + 0m = [0, 5]$

$\displaystyle b - m = [-2, 6]$

$\displaystyle b - 2m = [-4, 7]$

$\displaystyle b - 3m = [-6, 8]$

b) Graph all 7 vectors in part a with tail at $\displaystyle [0, 0]$

c) Explain the pattern in the results.------- Does this mean the graph increases or decreases 2 units for the x values and the y values goes increases or decreases 1 unit? ----------- If I'm correct, is there a correct term to use for it?

d) How would the above results be affected if vector b were replaced with each vector?------ I don't see a pattern for the next two. . .Do I use a specific formula to find the pattern?

i)$\displaystyle b = [2,4]$

$\displaystyle b + 3m = [8, 11]$

$\displaystyle b + 2m = [8, 7]$

$\displaystyle b + m = [4, 3]$

$\displaystyle b + 0m = [2, -1]$

$\displaystyle b - m = [0, -5]$

$\displaystyle b - 2m = [-2, -9]$

$\displaystyle b - 3m = [-4, -13]$

ii)$\displaystyle b = [-1, 2]$

$\displaystyle b + 3m = [-1, 5]$

$\displaystyle b + 2m = [0, 3]$

$\displaystyle b + m = [1, 1]$

$\displaystyle b + 0m = [2, -1]$

$\displaystyle b - m = [3, -3]$

$\displaystyle b - 2m = [4, -5]$

$\displaystyle b - 3m = [5, -7]$