The line has slope is .

The line passes through the point .

The point slope form of a line equation is.

Substitute .

The line equation is .

(a) Find the distance between line and  as a function of .

The perpendicular distance between line and a point is .

The line equation is .

The point is .

Substitute , ,  and  in .

.

(b)

Graph:

Graph the equation .

(c) Find  and .

Consider .

.

.

As  approaches to , the distance approaches .

Consider.

.

.

As  approaches to , the distance approaches .

(a) .

(b)

Graph:

Graph the equation .

(c)  and .

As  approaches to , the distance approaches .