Answer :
To determine the value of \( b \) for the point \( (b, 2.5) \) that lies on the line given by the equation \( 2y = 5x + 4 \), we can substitute \( y \) with \( 2.5 \) and solve for \( x \):
Given:
\[ 2y = 5x + 4 \]
Substitute \( y \) with \( 2.5 \):
\[ 2(2.5) = 5x + 4 \]
\[ 5 = 5x + 4 \]
Now, solve for \( x \):
\[ 5x = 5 - 4 \]
\[ 5x = 1 \]
\[ x = \frac{1}{5} \]
So, the value of \( b \) is \( \frac{1}{5} \) or \( 0.2 \). Therefore, the point is \( (0.2, 2.5) \).