Determine the vector and parametric equations for the line passing through the points P(-1,-3) and Q(3,5). a) r=(3,5) + s(1,2), seR      x=2t-1, y=4t-3, teR b) r=(1,-3) + s(4,8), seR      x=4t-1, y=8t-3, teR c) r=(1,0) + s(2,4), seR     x= t-1, y=2t-3, teR d) all of the above

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A line is determined by 2 points. If both P and Q satisfies the equation, it is an equation of the line.

 

a) (-1,-3)=(3,5)+s(1,2) for s=-4 P belongs to the line

(3,5)=(3,5)+(1,2) for s=0 Q belongs to the line therefore

It is a vector equation of the line (PQ)

 

3=2t-1, 5=4t-3  for t=2 therefore the coordinates of Q satisfy the equation.

(The entire section contains 203 words.)

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