To graph: The equation x = 2 y + 12 and check the equation for symmetry.

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 114RE
To determine

To graph: The equation x=2y+12 and check the equation for symmetry.

Expert Solution

The equation x=2y+12 is not symmetric and the graph is as follows:

Explanation of Solution

Given information:

The equation of line x=2y+12

Formula used:

The equation is said to have symmetry about the x -axis when the equation remains unchanged on replacing y by y

Graphically it can be said that the graph remains unchanged when reflected in the x -axis.

The equation is said to have symmetry about the y -axis when the equation remains unchanged on replacing x by x

Graphically it can be said that the graph remains unchanged when reflected in the y -axis.

The equation is said to have symmetry about the origin if it is symmetric about x -axis and y -axis that is the equation remains unchanged on replacing x by x or y by y

Graphically it can be said that the graph remains unchanged when rotated with an angle of 180 about the origin.

Calculation:

It is provided that the equation of line is x=2y+12 (1)

Firstly replace y by y in (1)

x=2(y)+12x=2y+12

The equation obtained is not the same as the original one.

Hence, x=2y+12 is not symmetric about x -axis

Next, replace x by x in (1)

x=2y+12x=2y12

The equation obtained is not the same as the original one.

Hence, x=2y+12 is not symmetric about y -axis.

Thus, x=2y+12 is not symmetric about origin.

For plotting:

 x x=2y+12 (x.y) 246 −5−4−3 (2,−5)(4,−4)(6,−3)

We plot these points to get the graph as follows:

Thus, x=2y+12 is neither symmetric about x -axis nor about y -axis.

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