Answer :
Given the equation of the line in slope-intercept form:
[tex]y=mx+b[/tex]where 'm' defines the slope of the line, we can find the perpendicular slope using the following expression:
[tex]m_p=-\frac{1}{m}[/tex]In this case, we have the following equation of the line:
[tex]y=-\frac{1}{6}x-3[/tex]notice that the slope is m = -1/6. Then, using the expression for the perpendicular slope, we have:
[tex]\begin{gathered} m_p=-\frac{1}{-\frac{1}{6}}=6 \\ m_p=6 \end{gathered}[/tex]therefore, the equation of the line that is perpendicular to y = -1/6x - 3 is:
[tex]y=6x+1[/tex]