Answer:
A parallel line would have a slope of [tex]-\frac{7}{6}[/tex] while a perpendicular would have a slope of [tex]\frac{6}{7}[/tex].
Step-by-step explanation:
Convert this equation to slope-intercept format ([tex]y=mx+b[/tex]):
[tex]-7x-6y=4\\-7x+7x-6y=4+7x\\-6y=7x+4\\\frac{-6y}{-6} =\frac{7x}{-6}+\frac{4}{-6} \\y = -\frac{7}{6}x-\frac{2}{3}[/tex]
In this case, your slope is [tex]-\frac{7}{6}[/tex].
A parallel line, by definition, will have the same slope as your original line; otherwise, the lines would eventually touch, which would render them not parallel.
A perpendicular line, on the other hand, must form four 90-degree angles when it intersects the original line, that is, it must cross it at an exact slope; that slope is the opposite reciprocal of the slope for the original line. Simply put, invert the sign and flip the fraction. In this case:
[tex]Original = -\frac{7}{6}\\Perpendicular = \frac{6}{7}[/tex]
