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Section 1.2
Graphs of Equations In Two Variables;
Intercepts; Symmetry
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Determine if the following points are on the graph of the equation 3x +y = 6
(b) (2, 0)(a) (0, 4) (c) (1, 3)
0 43 4 6 3 62 0 3 3 61 33
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Find the x-intercept(s) and the y-intercept(s) of the graph of then graph by plotting points.
2 4y x
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
If a graph is symmetric with respect to the x-axis and the point (3,2) is on the graph, what other point is also on the graph?
(3,2)
(3,2)
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
If a graph is symmetric with respect to the y-axis and the point (3,2) is on the graph, what other point is also on the graph?
( 3, 2) (3,2)
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
If a graph is symmetric with respect to the origin and the point (3,2) is on the graph, what other point is also on the graph?
( 3, 2)
(3,2)
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
2
2
9Test for symmetry.2
xyx
x-Axis: 2
2
92
xyx
Not equivalent so not symmetric with respect to the x-axis.
y-Axis:
2
2
9
2
xy
x
IS equivalent so symmetric with respect to the y-axis.
Origin:
2
2
9
2
xy
x
Not equivalent so not symmetric with respect to the origin.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.