To find the slope between two points, we use the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where $(x_1, y_1)$ and $(x_2, y_2)$ are the two points. Given the points $(\frac{3}{4}, 6)$ and $(\frac{5}{2}, 1)$, we can substitute:

$x_1 = \frac{3}{4}, \, y_1 = 6, \, x_2 = \frac{5}{2}, \, y_2 = 1$

Now substitute into the slope formula:

$m = \frac{1 - 6}{\frac{5}{2} - \frac{3}{4}}$

Simplify the numerator and denominator:

1. $1 - 6 = -5$
2. $\frac{5}{2} - \frac{3}{4} = \frac{10}{4} - \frac{3}{4} = \frac{7}{4}$

So, the slope becomes:

$m = \frac{-5}{\frac{7}{4}} = -5 \times \frac{4}{7} = \frac{-20}{7}$

Thus, the slope of the line through the points $(\frac{3}{4}, 6)$ and $(\frac{5}{2}, 1)$ is $\frac{-20}{7}$.

Would you like further details or clarification? Here are some related questions:

1. How do you interpret the slope of a line in a real-world context?
2. How does the slope change if the points are farther apart?
3. What happens to the slope if the line is horizontal or vertical?
4. How can we use the slope to write the equation of a line?
5. What is the meaning of a negative slope in terms of direction?

Tip: When subtracting fractions, always find a common denominator to make the calculation easier.