Answer:
6x + y = -1
Explanation:
The general slope-intercept form of the equation of a line is given as;
[tex]y=mx+b[/tex]
where m = slope of the line
b = y-intercept
Given the below equation of a line;
[tex]y=\frac{1}{6}x-1[/tex]
we can see that the slope of the line, m = 1/6 and the y-intercept, b = -1
Any line that will be perpendicular to the above line must have a negative reciprocal of its slope. So if the slope of the given line is 1/6, then the slope of the perpendicular line will be;
[tex]-\frac{1}{(\frac{1}{6})}=-1\ast\frac{6}{1}=-6[/tex]
So the slope of the perpendicular is -6, the equation of the line can then be written as;
[tex]\begin{gathered} y=-6x-1 \\ \end{gathered}[/tex]
Looking at the given options in the question, we'll need to rewrite the above equation;
Let's add 6x to both sides of the equation, we'll have;
[tex]\begin{gathered} 6x+y=6x-6x-1 \\ 6x+y=-1 \end{gathered}[/tex]
