Question

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

Answer 1

Answer:

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

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;

$y=\frac{1}{2}x-2$

The slope of this line is $\frac{1}{2}$

The slope of the line perpendicular to this line is the negative reciprocal of the $\frac{1}{2}$.

Hence; $m=-\frac{1}{\frac{1}{2} } =-2$

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

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