Slope and (x, y) Intercept

Date: 02/19/99 at 09:47:48
From: Alison Willey
Subject: Slope and (x, y) Intercept

Our math teacher asked us to do a report on the following question:

Does slope depend on (x, y) intercept or does (x, y) intercept depend 
on slope? I have no idea how to go about answering this question.

Sincerely,
Alison Willey

Date: 02/19/99 at 10:17:39
From: Doctor Rob
Subject: Re: Slope and (x, y) Intercept

Here are some thoughts that might help.

You are asked about the two following scenarios:

  1. You are given the x- and y-intercepts of a line, and you want
     to find the slope.

  2. You are given the slope of a line, and you want to find the 
     x- and y-intercepts.

In scenario 2, think of a whole family of lines with the same slope.
They are parallel to each other. Each has a different pair of 
intercepts.

In scenario 1, think of the intercept points. Remember that two 
distinct points determine a line. Can the two intercept points be the 
same point (that is, can they coincide)?

What is the x-intercept of the line y = 0? What is the x-intercept of 
the lines y = 1? What is the y-intercept of the line x = 0? What is the 
y-intercept of the line x = 1?

Are vertical lines allowed here, that is, ones with infinite slope?
How about horizontal lines?

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/