How do you write a vector equation with the given info?

How do you write a vector equation of the line that passes through (6, 1) with a slope of -2/3?|||If the slope is -2/3, this means it is "rise/run" or Δy / Δx. Therefore, we can split this up into x and y components:





Δy = -2


Δx = 3





And make a vector out of them:





%26lt;Δx,Δy%26gt;


%26lt;3,-2%26gt;.





Now that we have our slope vector, and our initial position vector, %26lt;6,1%26gt;, we can write the equation of a line.





r(t) = r0 + v*t


r(t) = %26lt;6,1%26gt; + %26lt;3,-2%26gt;t


r(t) = %26lt;6,1%26gt; + %26lt;3t, -2t%26gt;


r(t) = %26lt;(3t + 6), (1 - 2t)%26gt;