Download Plotting Ordered Pairs

Math 52
3.1"Graphs and Applications of Linear Equations"
Objectives:
*
Plot points associated with ordered pairs of numbers; determine the quadrant in which a point lies.
*
Find the coordinates of a point on a graph.
*
Determine whether an ordered pair is a solution of an equation with two variables.
*
Graph linear equations.
Plotting Ordered Pairs
In Chapter 2; we graphed numbers and inequalities in one variable on a line. To enable us to graph an equation
that contains two variables, we now learn to graph number pairs on a plane. The idea of associating an ordered pair of
numbers with points on a grid is attributed to the 17th century French mathematician Rene Descartes. Such a grid is called:
Rectangular (Cartesian) Coordinate System.
The point where the axes intersect is called
. The two axes
form a
and divide it into four regions called
: Every point on a coordinate plane can be identi…ed by an
of real numbers x and y;written as:
:
The …rst coordinate of an ordered pair is always graphed in a
and the second coordinate is always graphed in a
direction.
Example 1:
(Plotting points)
Graph the following points:
6
a) (2; 5)
b) (0; 3)
c) ( 4; 1)
4
2
-6
-4
-2
2
4
6
-2
-4
-6
Example 2:
In which quadrant, if any, are the points ( 5; 1) ; (2; 4) ; (0; 2) ; and (5; 0) located?
Page: 1
Notes by Bibiana Lopez
Introductory Algebra by Marvin L. Bittinger
3.1
Finding Coordinates
To …nd the coordinates of a point, we see how far to the right or left of zero it is located and how far up or down from
zero.
Example 3: (Finding coordinates)
Find the coordinates of points A; B; C; D; E and F:
Solutions of Equations
Now we begin to learn how graphs can be used to represent solutions of equations. When an equation contains two
variables, the solutions of the equation are ordered pairs in which each number in the pair corresponds to a letter in the
equation. Unless stated otherwise, to determine whether a pair is a solution, we use the …rst number in each pair to replace
the variable that occurs …rst alphabetically.
Example 4: (Solutions of equations)
Determine whether the given ordered pair is a solution of the equation.
a) (4; 2) ; 2x + 3y = 12
b) ( 5; 1) ;
2p
3q =
13
Graphs of Linear Equations
Any equation equivalent to one of the form
or
b; A; B; and C are constants (not variables) and A and B are not both 0; is a linear equation.
, where m;
Graph of an Equation:
kThe graph of an equation is a drawing that represents all its solutions.k
To Graph a Linear Equation:
1: Select a value for one variable and calculate the corresponding value of the other variable.
2: Repeat step (1) to obtain at least two other ordered pairs.
3: Plot the ordered pairs and draw a straight line passing through the points.
Note:
Two points are essential to determine a straight line. A third point serves as a check.
Page: 2
Notes by Bibiana Lopez
Introductory Algebra by Marvin L. Bittinger
Example 6: (Graphing linear equations)
Graph the following linear equations.
a) y = 2x 3
x
y
3.1
b) 2y + 3x = 12
(x; y)
x
y
y
y
(x; y)
10
6
4
5
2
-6
-4
-2
2
4
6
-2
-10
x
-5
5
10
x
-5
-4
-6
-10
c) 3y + 5x = 0
x
y
d) 3y
6x = 9
x
(x; y)
y
y
-6
-4
(x; y)
y
6
6
4
4
2
2
-2
2
-2
4
6
-6
x
-4
-2
2
-2
-4
-4
-6
-6
Page: 3
4
6
x
Notes by Bibiana Lopez