Final answer:
Without proper constraints or objective functions, it is impossible to determine the extreme points for the solution set. However, the slope between points (1, 0.1) and (7, 26.8) is approximately 4.5.
Step-by-step explanation:
The provided question seems to pertain to the identification of extreme points for a solution set in a geometrical context, which can be understood within the realm of linear programming or graphical analysis of systems of inequalities. However, the given points (a-f) cannot be evaluated without the corresponding system of constraints or objective function. Extreme points in linear programming are the vertices of the feasible region defined by the constraints where the objective function achieves its maximum or minimum values.
Regarding the slope calculation mentioned in the question, the slope of a line passing through the points (1, 0.1) and (7, 26.8) can be calculated using the formula slope (m) = (y2 - y1) / (x2 - x1). After substituting the coordinates we get m = (26.8 - 0.1) / (7 - 1) = 26.7 / 6 = 4.45, which can be rounded to 4.5 as the closest answer choice.