We are given the parametric equations:

$x = t + 7$

$y = t$

Step 1: Express $t$ in Terms of $y$

From the second equation, we solve for $t$:

$t = y$

Step 2: Substitute into $x$

Substituting $t = y$ into the first equation:

$x = y + 7$

Thus, the rectangular equation is:

$x = y + 7$

or equivalently,

$y = x - 7$

Step 3: Determine the Domain

The original parametric equations do not impose any restrictions on $t$ (i.e., $t$ can take any real number value). Since $y = t$, this means $y$ can also take any real number, and therefore, $x = y + 7$ can also take any real number.

Since there are no restrictions on $t$, the domain of the rectangular equation remains all real numbers.

Final Answer:

$\text{NOT NECESSARY}$

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Would you like a more detailed explanation or any clarifications?

Here are five related questions to expand on this topic:

1. How do you determine the domain of a function given in parametric form?
2. What are the steps to eliminate a parameter from a set of parametric equations?
3. Can parametric equations define functions that are not expressible as a single function in rectangular form?
4. How would the domain change if the parametric equations included square roots or denominators?
5. How can parametric equations be used to represent curves that a rectangular equation cannot?

Tip: When converting parametric equations to rectangular form, always check whether the resulting function has any domain restrictions imposed by the parameter!