To determine if the point \((\frac{1}{2}, -\frac{3}{2})\) is a solution to the inequality \(y > \frac{4}{5}x - 3\), we will substitute \(x = \frac{1}{2}\) and \(y = -\frac{3}{2}\) into the inequality and see if it holds true.
First, we calculate the right side of the inequality:
\[ \frac{4}{5}x - 3 = \frac{4}{5} \cdot \frac{1}{2} - 3 = \frac{4}{10} - 3 = \frac{2}{5} - 3 = \frac{2}{5} - \frac{15}{5} = \frac{2 - 15}{5} = \frac{-13}{5} \]
Now we need to compare \(-\frac{3}{2}\) with \(-\frac{13}{5}\).
Convert \(-\frac{3}{2}\) to a fraction with the same denominator of 10 for easier comparison:
\[ -\frac{3}{2} = -\frac{15}{10} \]
Now compare: \[ -\frac{15}{10} \quad \text{and} \quad -\frac{26}{10} \]
Since \(-\frac{15}{10} > -\frac{26}{10}\), it means:
\[ -\frac{3}{2} > \frac{4}{5} \cdot \frac{1}{2} - 3 \]
Therefore, the point \((\frac{1}{2}, -\frac{3}{2})\) does satisfy the inequality \(y > \frac{4}{5}x - 3\).
So, the answer is \(1\) for yes.