Question

Consider the line passing through the points (2, 1) and (-2, 3). Find the parametric equation for y if x = t + 1.

Answer 1

Find the line that pass through the two points P1(2,1), and P2(-2,3) in rectangular coordinates:
(x2-x1)(y-y1)=(y2-y1)(x-x1)
(-2-2)(y-1) = (3-1)(x-2)
-4(y-1) = 2(x-2)
2y+x=4
Solve for y in terms of x:
y=-x/2 + 2
substitute x=t+1
y=-(t+1)/2+2
=-t/2 + 3/2
So:
x=t+1
y=t/2 + 5/2