It is given that the line is perpendicular to the line y=2x+7.
Slope of given line=2.
Let the slope of required line be m.
Since the required line is perpendicular to the given line, so it follows:
[tex]m=-\frac{1}{2}[/tex]Since the product of slopes of perpendicular lines is -1.
It is also given that the line passes through (-2,4) so by slope-point form, the equation is given by:
[tex]\begin{gathered} y-4=-\frac{1}{2}(x-(-2)) \\ 2y-8=-(x+2) \\ 2y-8=-x-2 \\ x+2y-6=0 \end{gathered}[/tex]So the equation is x+2y-6=0.
