Final answer:
The slope of a line through points (1, 0.1) and (7, 26.8) is 4.5, which is different from the slope of a hyperbola as the latter changes at every point. The center of a hyperbola does not determine its slope on the upper left side without additional information.
Step-by-step explanation:
The question seems to be asking about the features of a hyperbola with a given center and slope. However, there is confusion as the slope of a hyperbola is not constant as it is with a line. The slope of a line is constant and can be found using two points on the line. For example, to find the slope of a line passing through points (1, 0.1) and (7, 26.8), we would use the slope formula (difference in y-coordinates divided by the difference in x-coordinates).
The calculation for the slope would be as follows:
m = (y2 - y1) / (x2 - x1)
m = (26.8 - 0.1) / (7 - 1)
m = 26.7 / 6
m = 4.45, which can be rounded to 4.5 as per the options provided.
Regarding the hyperbola, without specific information about its axes or asymptotes, we cannot determine the precise geometry or slope on the upper left side from the center (7, -3). In general, the slopes of the tangents to a hyperbola change at every point, depending on the curvature and orientation of the hyperbola.