Consider the line \( 9 x-4 y=-9 \). What is the slope of a line perpendicular to this line? What is the slope of a line parallel to this line? Slope of a perpendicular line: Slope of a parallel line:

To find the slope of the line given by the equation \( 9x - 4y = -9 \), we first need to rewrite it in slope-intercept form, which is \( y = mx + b \) where \( m \) is the slope. Rearranging the equation gives us \( 4y = 9x + 9 \), or \( y = \frac{9}{4}x + \frac{9}{4} \). Thus, the slope of this line is \( \frac{9}{4} \). The slope of a perpendicular line is the negative reciprocal of the original slope. Therefore, the slope of a line perpendicular to this line is \( -\frac{4}{9} \). However, a parallel line will have the same slope as the original line. This means the slope of a line parallel to this line is also \( \frac{9}{4} \). So, the answers are: Slope of a perpendicular line: \(-\frac{4}{9}\) Slope of a parallel line: \(\frac{9}{4}\)