Find and interpret the average rate of change illustrated in each graph.
$Line graph showing amount saved in dollars increasing steadily from \$0 to \$200 over 4 months.$

Verified step by step guidance

Step 1: Identify two points on the graph to calculate the average rate of change. For example, use the points (2, 90) and (8, 360).

Step 2: Recall the formula for the average rate of change between two points $(x_1, y_1)$ and $(x_2, y_2)$:

\[\text{Average Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}\]

Step 3: Substitute the coordinates of the chosen points into the formula:

\[\frac{360 - 90}{8 - 2}\]

Step 4: Simplify the expression to find the average rate of change, which represents the change in carbon production rate per year.

Step 5: Interpret the result as the average increase in Company X's bi-yearly carbon production rate (in tonnes) for each year over the 8-year period.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Average Rate of Change

The average rate of change measures how much a quantity changes, on average, between two points. It is calculated as the change in the output (y-values) divided by the change in the input (x-values). In this context, it shows how the carbon production rate changes per year.

Interpreting Coordinates on a Graph

Each point on the graph represents a specific year and the corresponding carbon production rate. Understanding these coordinates helps in calculating the rate of change and interpreting real-world data, such as how production increases over time.

Linear Relationships

A linear relationship is shown by a straight line on the graph, indicating a constant rate of change. Here, the straight line connecting the points suggests that the carbon production rate increases steadily over the years.

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