pres Finding slopes of lines parcllel and perpendioular to a line given in the Consider the line \( 4 x+7 y=5 \). What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line: \( \square \) Slope of a perpendicular line: \( \square \)

To find the slopes of lines parallel and perpendicular to the given line \( 4x + 7y = 5 \), we first need to rearrange it into slope-intercept form \( y = mx + b \), where \( m \) is the slope. Rearranging gives us: \[ 7y = -4x + 5 \] \[ y = -\frac{4}{7}x + \frac{5}{7} \] From this equation, we see that the slope of the line is \( -\frac{4}{7} \). Therefore, the slope of a parallel line is \( -\frac{4}{7} \). For a perpendicular line, the slope is the negative reciprocal of the original slope. Thus, the slope of a perpendicular line is: \[ m_{\perpendicular} = \frac{7}{4} \] Slope of a parallel line: \( -\frac{4}{7} \) Slope of a perpendicular line: \( \frac{7}{4} \)