The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Given the equation of the line "g":
[tex]y=-10x-2[/tex]You can identify that:
[tex]\begin{gathered} m_g=-10 \\ b_g=-2 \end{gathered}[/tex]By definition the slopes of perpendicular lines are opposite reciprocals. Then, the slope of the line "h" is:
[tex]m_h=\frac{1}{10}[/tex]Knowing a point on the line "h" and its slope, you can substitute them into the equation
[tex]y=m_hx+b_h[/tex]And solve for the y-intercept:
[tex]\begin{gathered} 1=\frac{1}{10}(4)+b_h \\ \\ 1=\frac{2}{5}+b_h \\ \\ b_h=\frac{3}{5} \end{gathered}[/tex]Then, the equation of the line "h" is:
[tex]y=\frac{1}{10}x+\frac{3}{5}[/tex]