### Video Transcript

Daniel wants the graph the parametric curve defined by the equations π₯ is equal to π‘ plus one and π¦ is equal to five π‘ minus one for π‘ is greater than or equal to negative two and π‘ is less than or equal to two. Determine the coordinates of the point on the curve where π‘ is equal to one.

Weβre told that Daniel is trying to sketch a graph of the parametric curve defined by a pair of parametric equations. Weβre told π₯ is equal to π‘ plus one and π¦ is equal to five π‘ minus one. And weβre told that our values of π‘ range from negative two to two. We need to determine the coordinates that this parametric curve will have when our value of π‘ is equal to one.

The first thing worth pointing out is, this value of π‘ is indeed within our range of values of π‘. So, this is a valid value of π‘. Next, to find the coordinates of our parametric curve, we need to recall what we mean by parametric equations. Weβre given functions for π₯ and π¦ in terms of π‘. Weβre told π₯ is equal to π‘ plus one and π¦ is equal to five π‘ minus one. We can input values of π‘, and these will output the π₯- and π¦-coordinate for this value of π‘.

So, we need to substitute π‘ is equal to one into both of these expressions. Letβs start with substituting this into π₯ is equal to π‘ plus one. Substituting π‘ is equal to one, we get π₯ is equal to one plus one, which we can calculate is equal to two. We can do the same for π¦. Substituting π‘ is equal to one, we get five times one minus one, which simplifies to give us five minus one, which we can calculate is equal to four.

So, when π‘ is equal to one, our π₯-coordinate is two and our π¦-coordinate is four. And we write this as the Cartesian coordinates two, four. Therefore, we were able to show when π‘ is equal to one, the parametric curve defined by the equations π₯ is equal to π‘ plus one and π¦ is equal to five π‘ minus one will have coordinates two, four.