Question

Let |x| + |y| = c where, c is s real number. Determine the number of points that would be on the graph of the equation for each given cases:

Case 1: c < 0
Case 2: c = 0
Case 3: c > 0

Answer 1

1. 0
2. 1
3. an infinite number

Explanation:

Case 1

The absolute value of a number will not be negative, so the function is the sum of two non-negative numbers. That sum cannot be negative, so there will be no points on the graph.

Case 2

The sum of two non-negative numbers can be zero if they both are zero. This graph will have exactly one point: (x, y) = (0, 0). (In the attached, it doesn't show up.)

Case 3

There are an infinite number of ways two non-negative numbers can sum to a positive number. There will be an infinite number of points on the graph. The line segments in the attached graph illustrate that for c = 1.