Graph Analysis: Determining Uniform vs Non-uniform Rate of Change

Given the following graph, determine whether the rate of change is uniform or not

To determine whether the rate of change in the graph is uniform, we must analyze the graph for consistency in slope across its span:

• Step 1: Observe the graph shape.
• Step 2: Check where the line is straight, showing no change in slope, and where it curves or changes slope, indicating non-uniform change.

Now, let's work through these steps:

Step 1: By visually inspecting the graph, note that it does not form a perfectly straight line but rather curves upwards. This indicates variability in the slopes along the graph.

Step 2: Since the graph curves, indicating that the slope is not the same throughout, we conclude that the rate of change is not constant.

The curvature implies that the rate of change is non-uniform, as it varies at different points along the x-axis. Therefore, the slope is inconsistent, confirming non-uniformity.

Therefore, the graph shows a non-uniform rate of change.