Examine solutions to an absolute value equation

Let |x| + |y| = c, where c is a real number.

Determine the number of points that would be on the graph of the equation for each given case:
Case 1:  c < 0
Case 2:  c = 0
Case 3:  c > 0

Justify your answers.

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Absolute value is the distance a number is away from zero.

Given |x| + |y| = c, then c is positive or zero since both absolute values will be positive.

If c < 0, there are no solutions, or no points on the graph, since c is positive or zero.
If c = 0, there is one solution, or one point on the graph, where x and y are both equal to zero.
If c > 0, there are infinite solutions, or an infinite number of points on the graph.

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