Solve the following system of linear equations Find the parametric equation of the line through a and parallel to b

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A point M is on the line iff the vector `vec(aM)` is parallel to b.

Hopefully b is a non zero vector! 

M is on the line iff there exists a real t such that `vec(aM)=t*b`

If the coordinates of a are `(x_a, y_a)` and the coordinates of b are `(x_b, y_b), `

 

M(x,y) is on the line iff there exists a real t such that `x-x_a=t*x_b` and `y-y_a=t*y_b`
. It is a parametric system of equation of the line passing through a and parallel to b. The parameter is t

Answer: `x-x_a=t*x_b` and `y-y_a=t*y_b`

 

 

 

 

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