### Video Transcript

Give the parametric equation of the
line on point two, negative four, four with direction vector one, negative one,
five.

We begin by recalling that the
parametric equations of a line are as follows. 𝑥 is equal to 𝑥 sub zero plus
𝑡𝐥, 𝑦 is equal to 𝑦 sub zero plus 𝑡𝐦, and 𝑧 is equal to 𝑧 sub zero plus
𝑡𝐧, where 𝑥 sub zero, 𝑦 sub zero, 𝑧 sub zero is a point that lies on the
line. And the vector 𝐥, 𝐦, 𝐧 is a
direction vector of the line. We also have the parameter 𝑡,
which is a scalar quantity. In this question, we are told that
the point two, negative four, four lies on the line. So these will be the values of 𝑥
sub zero, 𝑦 sub zero, and 𝑧 sub zero, respectively. We are also given a direction
vector one, negative one, five, which will be the values of 𝐥, 𝐦, and 𝐧.

Substituting the values of 𝑥 sub
zero and 𝐥, we have 𝑥 is equal to two plus 𝑡. Next, we have 𝑦 is equal to
negative four minus 𝑡. Finally, substituting the values
four and five for 𝑧 sub zero and 𝐧, we have 𝑧 is equal to four plus five 𝑡. The parametric equation of the line
on point two, negative four, four with direction vector one, negative one, five is
as shown.