Question

Identify whether the graph displays a linear or nonlinear function. Explain why.

Graph A

On a coordinate plane, graph A goes through points (0, negative 3) and (2, 1).

Graph A displays a

Answer 1

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:

1. **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: \(m = \frac{4}{2} = 2\)

2. **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.