Algebra Honors (periods 5 & 6)

Points, Lines, and Their Graphs 8-2

We reviewed graphing or plotting an ordered pair as a point on a coordinate plane.
Horizontal axis is the x-axis
vertical axis is the y-axis

origin is at (0,0)

an ordered pair (3,2) lists the coordinates of a point. In this instance we called the Point A
3 is the x-coordinate also know as the abscissa of A
2 is the y-coordinate also known as the ordinate of A

the x- and y-axes are also called coordinate axes and the number plane is often called the coordinate plane. The coordinate axes separate a coordinate plane into four quadrants identified by Roman Numerals. See page 354 for details.
Points on the coordinate axes are NOT considered to be in any quadrant.

The graph of an equation in two variables consists of all the poins that are the graphs of the solutions of the equations.
x + 2y = 6 has the following ordered pairs:
(0,3)
(2,2)
(4,1)
(6,0)
There are infinite number of solutions-- such as
(-2,4)
(1, 2.5)
The graph of all the solutions lie on the straight line that is drawn when the points are connected.

x + 2y = 6 is a linear equation because its graph is a line.
All linear equations in the variables x and y can be written in the form
ax + by = c
or
Ax + By = C
where a, b, and c are real numbers with a and b noth both zero. If a, b, and c are integers, then the equation is said to be in standard form.

2x -5y = 7 and 4x + 9y = 0 and y = 3 are examples of linear equations in standard form

(1/2)x + 4y = 12 is not
y = 3x -1 is not
neither is x²y + 3y = 4
nor xy = 6

Although you only need two points to determine a line, I suggest you plot 3-- whenever possible to guard against mistakes.

The easiest solutions to find are those where the line crosses
the x-axis ( y = 0) and
the y-axis ( x = 0)

Math 6H ( Period 1, 2, & 3)

Points, Lines, Planes 4-1
We can describe but CANNOT DEFINE point, line or plane in Geometry

We use a single small dot to represent a point and in class we labeled with a P and we called it Point P
A straight line in Geometry is usually just called a line...
Two points DETERMINE exactly ONE LINE

we connected Point P with Point Q and created Line PQ
We placed this type of arrow ↔ over PQ to show a line
↔
PQ

that would represent the line PQ but we found we could write
↔
QP
and mean the SAME line!!

You can name ANY line with ANY TWO points that fall on that line!! USE only TWO points to name a line!!


Three or more points on the same line are called collinear. Notice the word "line" in collinear.
collinear

Points NOT on a same line are called noncollinear.

We have a RAY if we have an endpoint and it extends through other points. We name the rame by Naming the endpoint FIRST
→
PQ is RAY PQ and it begins at P and goes through Q. It is NOT the SAME as

→
QP which is Ray QP, which begins at Q and goes through P

Segments are parts of lines with TWO ENDPOINTS.
⎯
PQ is a segment with endpoints Point P and POint Q

We then looked at the drawing from page 105 and the class named all of the names for the line in the drawing, all of the rays that existed in the figure as well as the segments. We found that there were just 3 collinear points: A, X, B but that we could name 3 sets of non collinear points
X, Y, B and A, X, Y, AND A, B, Y

Three non-collinear points determine a flat surface called a plane.
We name a Plane by using three of its non collinear points!! Plane ABC was out example.

Lines in the same plane that do not intersect are PARALLEL lines. Two segments or rays are parallel if they are parts of parallel lines.
↔
AB is parallel to

↔
CD

may be written
↔ ↔
ABllCD
using two straight lines to indicate parallel

Parallel lines DO NOT intersect.

Intersecting lines intersect in a single point!!



Planes that do not intersect are called parallel planes... we looked around the room and found examples of parts of planes.. noticing which ones were parallel!! (the floor and ceiling were a great example)
Then we drew the box from PAge 106 and identified parallel segments and lines from that box.

Two non parallel lines that do not intersect are called SKEW LINES.