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Consider the line parametrized by  x = 2t + 1, y = -3t +2. Find a vector < a ; b > that's parallel to this line and satisfies a+b = 3.

May 9, 2019

$$\text{A line has the same slope at all points so }\\ m = \lim \limits_{t\to \infty}\dfrac{y(t)}{x(t)} = -\dfrac 3 2\\ \dfrac{b}{a}=-\dfrac 3 2\\ b=-\dfrac{3a}{2}\\ a+b=3\\ a+\left(\dfrac{-3a}{2}\right)=3\\ -\dfrac{a}{2}=3\\ a = -6\\ b = 9\\ <-6,9>$$