3.1 Constant Rate of Change

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What is a constant rate of change?

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A constant rate of change refers to a situation where the change in one quantity is consistent with the change in another quantity over a specific interval. It is often represented as a linear relationship.

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How can you identify a constant rate of change from a graph?

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A constant rate of change can be identified from a graph by observing a straight line, indicating that the relationship between the two variables is linear.

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What does a slope represent in the context of a constant rate of change?

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In the context of a constant rate of change, the slope of a line represents the rate at which one variable changes in relation to another.

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What is the formula for calculating the rate of change?

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The formula for calculating the rate of change is (change in y) / (change in x), often expressed as (y2 - y1) / (x2 - x1).

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What is the significance of the constant of proportionality?

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The constant of proportionality is the constant factor that relates two proportional quantities, indicating how much one quantity changes in relation to another.

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How do you determine the constant of proportionality from a table of values?

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To determine the constant of proportionality from a table of values, divide the value of one quantity by the corresponding value of the other quantity for any pair of values.

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What is an example of a real-world scenario that demonstrates a constant rate of change?

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An example of a real-world scenario that demonstrates a constant rate of change is the cost of a taxi ride, where the fare increases at a constant rate per mile.

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What is the relationship between constant rate of change and linear equations?

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The relationship is that a constant rate of change indicates a linear equation, which can be expressed in the form y = mx + b, where m is the slope.

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How can you verify if a table of values represents a constant rate of change?

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You can verify if a table of values represents a constant rate of change by checking if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

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What does a rate of change of 0 indicate?

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A rate of change of 0 indicates that there is no change in the dependent variable as the independent variable changes, resulting in a horizontal line on a graph.