Consider the line \( x-7 y=-5 \). 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:

The slope of a line parallel to \( x - 7y = -5 \) is the same as the original line's slope. To find the slope, let's rearrange the equation into slope-intercept form \( y = mx + b \). Rearranging gives us \( 7y = x + 5 \), or \( y = \frac{1}{7}x + \frac{5}{7} \). This means the slope \( m \) is \( \frac{1}{7} \). The slope of a line perpendicular to this line is the negative reciprocal of the original slope. Since the slope of the original line is \( \frac{1}{7} \), the slope of a perpendicular line would be \( -7 \) (as \( -\frac{1}{m} = -\frac{1}{\frac{1}{7}} = -7 \)). Slope of a parallel line: \( \frac{1}{7} \) Slope of a perpendicular line: \( -7 \)