11) The equation representing a straight line is \( 4 y=5 x+8 \). The slope of line is: \begin{tabular}{|l|l|}\hline a) \( \mathbf{1 . 2 5} \) & b) 5 \\ \hline\end{tabular}

To find the slope of the line given by the equation \( 4y = 5x + 8 \), first rearrange it into slope-intercept form \( y = mx + b \), where \( m \) is the slope. Dividing the entire equation by 4 gives \( y = \frac{5}{4}x + 2 \). Thus, the slope \( m \) is \( \frac{5}{4} \), which can also be expressed as \( 1.25 \). So, the correct answer is \( \mathbf{1.25} \) (Option a). In real-world contexts, slopes play a crucial role, like in financial graphs where a steeper slope indicates a rapid increase in profits over time. Understanding slopes also helps in planning, such as optimizing road inclinations for better vehicle movement or constructing roofs that effectively manage rainwater drainage.