+0

# Consider the line parametrized by \begin{align*} x&= 4t + 2,\\ y& = t+2. \end

0
207
1

Consider the line parametrized by$$x= 4t + 2, y = t+2$$
Find vector $$\begin{pmatrix}a\\b\end{pmatrix}$$ that's parallel to this line and satisfies $$a+b=10$$.

Feb 2, 2019

#1
+103947
+1

Here's my best effort....although there might be an easier method !!!

Wnen  = 0   we have the point (2, 2)

When t = 1  we have the point  (6, 3)

So...the slope of the given line is   (3 - 2) / (6 - 2) =  1/4

If we let the parallel line go through the origin....we have the line  y = (1/4)x

This means that  every point on this line has the coordinates ( x, 1/4x)

This implies that

x + (1/4)x = 10

(5/4)x = 10

x = 8   and y = (1/4)x = 2

So....the required vector  is    < 8, 2 >

Feb 2, 2019