Lecture-13-b

# Lecture-13-b - Lecture 13 (supplement) These notes exhibit...

This preview shows pages 1–2. Sign up to view the full content.

Lecture 13 (supplement) These notes exhibit a few ways of showing that: a) every line in the plane is the graph of a linear equation, and a) the graph of every linear equation is a line? The Frst demonstration, which is based on similar triangles, follows a pattern that can be found in expositions of analytic geometry in the early 18th century. I have found this argument repeated in algebra textbooks from the 1970s. The fat Algebra textbook of Sullivan, which was formerly used for Math 1021 at LSU, has a version of this, but it’s not presented carefully, and there is much hand-waving. Theorem 1. Suppose that P 0 = ( x 0 , y 0 ) and P 1 = ( x 1 , y 1 ) are points in the plane with x 0 n = x 1 . Let L be the line through P 0 and P 1 , and let m = y 1 y 0 x 1 x 0 . Then, for any point P = ( x, y ) in the plane: P is on L if and only if y y 0 = m ( x x 0 ) . (1) Proof. If y 1 = y 0 , then equation (1) reads y = y 0 and L is the line perpendicular to the y -axis through (0 , y 0 ). The conclusion in this case is immediate from the deFnition of the coordinate system. Let us turn to the situation when y 1 n = y

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/23/2011 for the course MATH 6302 taught by Professor Madden during the Summer '11 term at LSU.

### Page1 / 3

Lecture-13-b - Lecture 13 (supplement) These notes exhibit...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online