Question

Find the parametric equation of the line through `(0,3)` that is parallel to the line `x=-5+t, y=1-2t`.

Answer

Since line should be parallel, then its equation is `x=a+t, y=b-2t`.

Line passes through point `(0,3)`, so `0=a+t, 3=b-2t`.

If we take `t=0`, then `a=0, b=3`.

Thus, equation of the line is `x=t, y=3-2t`.

Answer: `x=t, y=3-2t`.