To define the translation from the point \((4, -1)\) to \((6, -1)\), we first need to identify the change in the x-coordinates, as the y-coordinate remains unchanged.
- The x-coordinate changes from \(4\) to \(6\), which is an increase of \(2\) units.
- The y-coordinate remains constant at \(-1\).
Therefore, the point can be translated using a translation function that reflects this change. In general, a translation in the coordinate plane can be represented as:
\[ T(x, y) = (x + a, y + b) \]
Where \((a, b)\) represents the translation vector. In this case:
- \(a = 2\) (the change in x)
- \(b = 0\) (the change in y)
Putting this into the translation function, we have:
\[ T(x, y) = (x + 2, y) \]
So the function that shows the translation from the point \((4, -1)\) to \((6, -1)\) is:
\[ T(x, y) = (x + 2, y) \]