Two lines are perpendicular when the multiplication of their slopes is equal to minus one. In the line:
[tex]y=4x+1[/tex]the slope is m1 = 4. Therefore, the slope, m2, of a line perpendicular to this one is:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ 4\cdot m_2=-1 \\ m_2=-\frac{1}{4} \end{gathered}[/tex]Equation of a line in point-slope form
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1, y1) is a point on the line.
Substituting with m = -1/4 and the point (-4, 2), we get:
[tex]\begin{gathered} y-2=-\frac{1}{4}(x-(-4)) \\ y-2=-\frac{1}{4}(x+4) \end{gathered}[/tex]