To determine the domain of a linear function defined by two points, we need to consider the nature of linear functions. A linear function is typically represented in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
In this case, the function is defined by the line passing through the points (5, -7) and (1, 0). The domain of a linear function is generally all real numbers, \((- \infty, \infty)\), because a linear function continues infinitely in both the positive and negative directions along the x-axis.
Therefore, the domain of the linear function defined by the red line that passes through points (5, -7) and (1, 0) is:
\[ (-\infty, \infty) \]