Question 1208024: Describe each of the following graphs in the -plane. Give justification.
A. x = 0
B. y = 0
C. x + y = 0
D. xy = 0
Let me see.
For A, the line x = 0 is the y-axis.
For B, the line y = 0 is the x-axis.
For C, the line x + y = 0 tells me that both x and y have the same number. One is negative and the other positive. It also tells me that x and y can both be zero.
For D, the line xy = 0 tells me that either x is 0 or y is 0.
You say?
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
Describe each of the following graphs in the -plane. Give justification.
A. x = 0
B. y = 0
C. x + y = 0
D. xy = 0
Let me see.
For A, the line x = 0 is the y-axis.
For B, the line y = 0 is the x-axis.
For C, the line x + y = 0 tells me that both x and y have the same number. One is negative and the other positive. It also tells me that x and y can both be zero.
For D, the line xy = 0 tells me that either x is 0 or y is 0.
You say?
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(A) is correct.
(B) is correct.
(C) To be more accurate, I would say that for (C), x and y have the same absolute values, but different signs.
The line x + y = 0 is the same as the line y = -x.
Geometrically, it is a straight line with the slope -1 through the origin of the coordinate system
which goes from upper left to down right, making the angle of 135 = 90 + 45 degrees with
the positive direction of x-axis.
(D) The graph of equation xy = 0 is the union of two straight lines.
One line is x-axis y= 0.
Another line is y-axis x= 0.
The graph also includes the origin of the coordinate system (0,0), which is the intersection of the two mentioned straight lines.
Solved.
I am glad to see your progress.
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