Answer:
[tex]f(x)=-2x+10[/tex]
Step-by-step explanation:
The given line passes through (6-2).
The given is perpendicular to 2y=x-4.
We solve for y in the given equation to get;
[tex]y=\frac{1}{2}x-2[/tex]
The slope of this line is [tex]\frac{1}{2}[/tex]
The slope of the line perpendicular to this line is the negative reciprocal of the [tex]\frac{1}{2}[/tex].
Hence; [tex]m=-\frac{1}{\frac{1}{2} } =-2[/tex]
The equation is given by
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point [tex](x_1,y_1)=(6,-2)[/tex] to obtain;
[tex]y--2=-2(x-6)[/tex]
Hence the required equation is;
[tex]y+2=-2x+12[/tex]
[tex]y=-2x+12-2[/tex]
[tex]y=-2x+10[/tex]
The function notation is
[tex]f(x)=-2x+10[/tex]
