Question

Write a parameterization for the curve in the xy-plane.
The line traced out from the point (3, −1) at t = 0 to the point (1, 6) at t = 1.

Answer 1

Use of Vectors. Let P[3,-1] when t=0 and Q[1,6] when t=1.
Then X=P+t*(Q-P) is a vector that starts at A when t=0 and ends at B when t=1.
Now simply break this equation into components and you will have you parametrization for the curve in the xy-plane.