Answer:
To find the slope between the points (3, 5) and (4, 7.25), you use the formula for slope:
\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\]
Substituting the coordinates:
\[m = \frac{{7.25 - 5}}{{4 - 3}}\]
\[m = \frac{{2.25}}{{1}} = 2.25\]
So, the slope between these two points is 2.25.
Similarly, for the points (4, 7.25) and (5, 9.5):
\[m = \frac{{9.5 - 7.25}}{{5 - 4}} = \frac{{2.25}}{{1}} = 2.25\]
And for the points (5, 9.5) and (5, 11.75):
\[m = \frac{{11.75 - 9.5}}{{5 - 5}}\]
Since the denominator is zero, this slope is undefined. The line is vertical, which means it has an undefined slope.
Overall, the slopes for the given data points are 2.25, 2.25, and undefined.
Explanation: