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 \(a+b=10\).
+102417 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 >
