To find the domain of the linear function represented by the points (-5, -7) and (1, 0), we first need to recognize that the linear function is defined by all points on the line extending infinitely in both directions.
However, if we are only considering the line segment defined by these two points, the domain is limited to the x-values of these endpoints.
The x-coordinate of the first point (-5, -7) is -5, and the x-coordinate of the second point (1, 0) is 1. Therefore, the domain of the linear function that connects these two points, as a segment, is:
\[ \text{Domain: } [-5, 1] \]
If we're considering the function as a whole line extending infinitely, the domain would be all real numbers:
\[ \text{Domain: } (-\infty, \infty) \]
But for the segment between the two points, stick with \([-5, 1]\).