To find the rate of change of \( y \) with respect to \( x \) in the equation \( 5x - 8y = 40 \), we can rewrite this equation in slope-intercept form, \( y = mx + b \), where \( m \) represents the slope of the line.
Starting with the equation:
\[ 5x - 8y = 40 \]
we can isolate \( y \):
- Subtract \( 5x \) from both sides:
\[ -8y = -5x + 40 \]
- Now, divide every term by \(-8\):
\[ y = \frac{5}{8}x - 5 \]
From the equation \( y = \frac{5}{8}x - 5 \), we see that the slope \( m \), which represents the rate of change of \( y \) with respect to \( x \), is:
\[ \frac{5}{8} \]
Thus, the rate of change of \( y \) with respect to \( x \) for the equation \( 5x - 8y = 40 \) is \( \frac{5}{8} \).