### Video Transcript

Straight line 𝐿 passes through the
point 𝑁 with coordinates three, four and has a direction vector 𝐮 equal to two,
negative five. Then the parametric equations of
line 𝐿 are what.

We begin by recalling that the
parametric form of the equation of a line passing through the point 𝑥 sub zero, 𝑦
sub zero and parallel to the direction vector 𝑎, 𝑏 is 𝑥 is equal to 𝑥 sub zero
plus 𝑎𝑡 and 𝑦 is equal to 𝑦 sub zero plus 𝑏𝑡. We are told in the question that
the straight line 𝐿 passes through the point with coordinates three, four. This means that our value of 𝑥 sub
zero is three and 𝑦 sub zero is equal to four. We are also given a direction
vector 𝐮 such that 𝑎 is equal to two and 𝑏 is negative five.

Substituting in our values of 𝑥
sub zero and 𝑎, we get 𝑥 is equal to three plus two 𝑡. And substituting the values of 𝑦
sub zero and 𝑏, we get 𝑦 is equal to four minus five 𝑡. It is important to note that we
could replace the letter 𝑡 with any other letter as the parameter. For example, 𝑥 is equal to three
plus two 𝑘 and 𝑦 is equal to four minus five 𝑘 is also a valid solution. We can therefore conclude that
these are the parametric equations of line 𝐿.