Consider the line \( 7 x+5 y=9 \). What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

To find the slope of the line given by the equation \( 7x + 5y = 9 \), we can rewrite it in slope-intercept form \( y = mx + b \) where \( m \) is the slope. Rearranging gives us \( 5y = -7x + 9 \) or \( y = -\frac{7}{5}x + \frac{9}{5} \). Thus, the slope of the original line is \( -\frac{7}{5} \). Now, lines that are parallel have the same slope, so a line parallel to this would also have a slope of \( -\frac{7}{5} \). Conversely, the slope of a line perpendicular to the original line is the negative reciprocal of the slope. Therefore, the slope of a line perpendicular to the given line is \( \frac{5}{7} \).