Transcript Ordered Pairs and the Coordinate Graph

Ordered Pairs and the
Coordinate Graph
Cartesian Plane
The Cartesian Coordinate
Plane
The Cartesian plane was
the brainchild of
French mathematician
Rene Descartes trying
to combine algebra
and geometry
together.
To explain Descartes method, first think of
using a map. If you are trying to find a
specific location you use reference points
around the outside of the map and trace down
and across to find your location. It’s like using
longitude and latitude.
You learned about basic (counting) number
lines back in elementary school.
Later on, you were introduced to zero and
negatives, which completed the number line.
Descartes took a second number line and
standing it on end, crossed the lines at zero to
form a grid like pattern.
The number lines when drawn like this, are
called “axes”. The horizontal line is called the
“x-axis”; the vertical line is called the “y-axis”.
By the way, the arrows at the ends of the axes
indicate the direction in which the numbers
are getting larger.
Each coordinate plane
is divided into
quadrants. Using the
“ordered pairs” or the
x- and y-axes you can
find a point on the
plane.
To plot an ordered pair,
begin at the origin, the
point (0, 0), which is the
intersection of the x-axis
and y-axis.
The first coordinate tells
how many units to move
left or right; the second
coordinate tells how many
units to move up and down.
X-coordinate move right
or left
y-coordinate move up or
down
(x, y)
The sign of the number
indicates which
direction to move.
Positive: up or right
Negative: down or left
order pairs – a pair of numbers used to locate
a point on a coordinate plane.
coordinate plane – a plane formed by the
intersection of a horizontal number line called
the x-axis and a vertical line called the y-axis.
x-axis – the horizontal axis on a coordinate
plane.
y-axis – the vertical axis on a coordinate
plane.
x-coordinate – the first number in an ordered
pair; it tells the units to move right or left
from the origin.
y-coordinate – the second number in an
ordered pair; it tells the units to move up or
down from the origin.
More definitions
origin – the point where the x-axis and the yaxis intersect on the coordinate plane.
graph of an equation – the set of all ordered
pairs that are solutions of the equation.
dependent variable – the y-coordinate of an
equation, which depends on what the x-value will
be. (in the equation y = 2x, the y-value depends
on what the value of x is.)
independent variable – the x-coordinate of an
equation, which when substituted will determine
what the y-value will be. (in the equation y = 2x,
the value of x will determine what the value of y
equals)
Draw this coordinate plane
on graph paper and label all
parts.
Graphing an Equation
Using ordered pairs
The good, the bad and the ugly.
When graphing you always use graph paper
and draw neatly.
NO HAND DRAWN GRAPHS
Complete the table of values to determine the
ordered pairs. Graph the equation on a
coordinate plane.
x
-2
-1
0
1
2
y = 2x + 3
y
(x, y)
Graph of the equation y = 2x + 3
X
-2
-1
0
1
2
Y = 2x + 3
2(-2) + 3 = -4 + 3 = -1
2(-1) + 3 = -2 + 3 = 1
2(0) + 3 = 0 + 3 = 3
2(1) + 3 = 2 + 3 = 5
2(2) + 3 = 4 + 3 = 7
Y
-1
1
3
5
2
(x, y)
(-2, -1)
(-1, 1)
(0, 3)
(1, 5)
(2, 7)
Make a table of values for the following
equations and graph each on the coordinate
graph.
y=x+1
y = 3x
y = 2x - 1
Cartography, the science of map making, is an
application of graphing on a coordinate plane.
Cartographers map a region of the surface of
the earth onto part of a plane.