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

slope: undefined

equation: x = p

y-intercept: there is none

slope of perpendicular: 0

Explanation:

points: (p, a), (p, -a)

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

The slope is undefined since the line is vertical.

equation: x = p

Since p ≠ 0, the vertical crosses the x-axis at a point that is not x = 0 and never intersects the y-axis, so the is no y-intercept.

A line perpendicular to he given line is a horizontal line.

slope = 0