Answer :

The point is (4,-3) and is perpendicular to y=-2x-4.

The slope is given , m=-2.

For the perpendicular line, the slope is

[tex]m_1\times m_2=-1[/tex][tex]m_1\times-2=-1[/tex][tex]m_1=\frac{1}{2}[/tex]

Now, then the general equation is

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the values.

[tex]y-(-3)=\frac{1}{2}(x-4)[/tex][tex]y+3=\frac{1}{2}(x-4)[/tex][tex]y=\frac{1}{2}x-\frac{4}{2}-3[/tex][tex]y=\frac{1}{2}x-2-3[/tex][tex]y=\frac{1}{2}x-5[/tex]

Hence the equation is determined as

[tex]y=\frac{1}{2}x-5[/tex]