The equation of a line in slope-intercept form looks like this:
[tex]y=mx+b[/tex]Where m is known as the slope. All lines that have the same slope m are parallel whereas a line perpendicular to y=mx+b has a slope given by -1/m.
In this case we have the line 5x-6y=1. We should write it in slope-intercept form. In order to do this we can add 6y to both sides and substract 1 from both sides:
[tex]\begin{gathered} 5x-6y+6y-1=1+6y-1 \\ 5x-1=6y \end{gathered}[/tex]Then we divide both sides by 6:
[tex]\begin{gathered} \frac{6y}{6}=\frac{5x-1}{6} \\ y=\frac{5}{6}x-\frac{1}{6} \end{gathered}[/tex]Then the slope of this line is 5/6.
AnswerFollowing what we stated above we have these answers:
The slope of a line parallel to this is 5/6.
The slope of a line perpendicular to this is -6/5.
