Graph A displays a linear function.
This is because a linear function is defined as one that can be represented by a straight line on a coordinate plane. The key characteristics of a linear function include:
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Constant Rate of Change: The slope between any two points on a linear graph remains constant. For example, in Graph A, the slope can be calculated between the two provided points (0, -3) and (2, 1):
- The change in y (rise) is: \(1 - (-3) = 4\)
- The change in x (run) is: \(2 - 0 = 2\)
- Thus, the slope (m) is: \(m = \frac{4}{2} = 2\)
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Straight Line: If you can draw a straight line that connects any two points on the graph, then the function is linear.
Since the points (0, -3) and (2, 1) yield a consistent slope indicating a straight line, Graph A is indeed a linear function.
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