Explanation:
A perpendicular line to the given line has its opposite and reciprocal slope.
The given line y = -1/4x - 6 has a slope of -1/4. Therefore the slope of a perpendicular line is 4:
[tex]y=4x+b[/tex]To find the y-intercept b we have to use the point. We replace x = -3 and y = 4 into the equation above and solve for b:
[tex]\begin{gathered} 4=4\cdot(-3)+b \\ 4=-12+b \\ b=4+12=16 \end{gathered}[/tex]Answer:
The equation of the perpendicular line is y = 4x + 16
