Download Chapter 13 Graphing Equations

Chapter 13 Graphing Equations
13.1 The Rectangular Coordinate System
Ordered pair
Coordinate
x-axis
y-axis
Origin
Quadrants
Graphing an Ordered Pair
To graph the point corresponding to a particular ordered pair (x,y), you must start at the origin and move
x units to the left or right (right if x is positive, left if x is negative), then move y units up or down (up if y is
positive, down if y is negative).
Completing Ordered Pair Solutions
In general, an ordered pair is a solution of an equation in two variables if replacing the variables by the
values of the ordered pair results in a true statement.
If you know one coordinate of an ordered pair that is a solution for an equation, you can find the other
coordinate through substitution and solving the resulting equation.
Find the x and y coordinates of A, B, C, D, E, F.
F
A
E
D
C
B
A(
,
)
B(
,
)
C(
,
)
D(
,
)
E(
,
)
F(
,
)
32
Example: Complete the ordered pair.
1. (3, ___) is a solution of the equation
2 + 5 = −4.
2. (3, ___) is a solution of the equation
3 − = −5.
13.2 Graphing Linear Equations
Linear Equation in Two Variables
A linear equation in two variables is an equation that can be written in the form Ax + By = C. Where A,
B, C are real numbers and A and B not both 0. This form is called standard form. The graph of a linear
equation in two variables is a straight line.
1. 2 −
= −4
2.
=
+3
Note: When graphing a linear equation in two variables, if it is
•
solved for y, it may be easier to find ordered pair solutions by choosing x-values. If it is
•
solved for x, it may be easier to find ordered pair solutions by choosing y-values.
33