Question

A line passes through the points (p, a) and (p, –a) where p and a are real numbers and p ≠ 0. Describe each of the following. Explain your reasoning.

slope of the line
equation of the line
y-intercept
slope of a line perpendicular to the given line

Answer 1

the slope of the line that passes through (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)

given

(p,a) and (p,-a)

slope=(-a-a)/(p-p)=-2a/0=undefined

means

the slope is undefined

x=something

(x,y)

(p,a)

x=p is the equation

the equation of a perpendicular line is y=k where k is any real number

the y intercept of y=k would be y=k or the pont (0,k)

Answer 2

line passes through the points (p, a) and (p, –a)
where p and a are real numbers and p ≠ 0
(p, a) and (p, –a) m = Cannot divide by ZERO, there is no slope to this Line.
slope of the line: no slope (does not exist)
equation of the line: x = p Perpendicular Line
slope of a line perpendicular to the given line: would be m = 0, horizontal Line y= 3
y- intercept: none