Question

Write the equation using functional notation . Through (6,-2) ; perpendicular to 2y=x-4

Answer 1

`f(x)=-2x+10`

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;

`y=(1)/(2)x-2`

The slope of this line is
`(1)/(2)`

The slope of the line perpendicular to this line is the negative reciprocal of the
`(1)/(2)`.

Hence;
`m=-(1)/((1)/(2) ) =-2`

The equation is given by

`y-y_1=m(x-x_1)`

We substitute the point
`(x_1,y_1)=(6,-2)` to obtain;

`y--2=-2(x-6)`

Hence the required equation is;

`y+2=-2x+12`

`y=-2x+12-2`

`y=-2x+10`

The function notation is

`f(x)=-2x+10`