What is the slope of a line perpendicular to the line whose equation is \( 5 x+3 y=8 \) ?

To determine the slope of a line perpendicular to the one given by the equation \( 5x + 3y = 8 \), first, we need to find the slope of the original line. By rearranging the equation into slope-intercept form (\( y = mx + b \)), we get: \( 3y = -5x + 8 \) \( y = -\frac{5}{3}x + \frac{8}{3} \) Here, the slope \( m \) is \( -\frac{5}{3} \). The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the slope of the line perpendicular to this one is: \( m_{perpendicular} = \frac{3}{5} \). Perfectly perpendicular, right? Just like how a knight and a bishop move in chess! For practical applications, understanding slopes, particularly perpendicular slopes, is essential in fields like architecture and engineering. When designing buildings or bridges, ensuring structures are not only aesthetically pleasing but also stable often involves calculating and applying perpendicular lines efficiently. This knowledge helps professionals create strong and functional designs while minimizing errors and optimizing materials used.