Additive and Multiplicative Relationships

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What is an additive relationship?

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An additive relationship is when one quantity increases or decreases by a constant amount, resulting in a linear relationship. For example, if you add 2 apples every day, the total number of apples is an additive relationship.

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What is a multiplicative relationship?

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A multiplicative relationship is when one quantity is multiplied by a constant factor, resulting in an exponential growth or decay. For example, if you double the number of cookies every hour, the total number of cookies is a multiplicative relationship.

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How can you represent an additive relationship in a table?

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In a table, an additive relationship shows a constant difference between consecutive values. For example, if you start with 5 and add 3 each time, the table would show: 5, 8, 11, 14.

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How can you represent a multiplicative relationship in a table?

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In a table, a multiplicative relationship shows a constant ratio between consecutive values. For example, if you start with 2 and multiply by 3 each time, the table would show: 2, 6, 18, 54.

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What is the equation for an additive relationship?

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The equation for an additive relationship can be written as y = mx + b, where m is the constant amount added, and b is the starting value.

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What is the equation for a multiplicative relationship?

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The equation for a multiplicative relationship can be written as y = a * b^x, where a is the starting value, b is the constant factor, and x is the number of times the factor is applied.

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What does the slope of a line represent in an additive relationship?

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The slope of a line in an additive relationship represents the rate of change or the constant amount added for each unit increase in x.

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What does the y-intercept represent in an additive relationship?

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The y-intercept in an additive relationship represents the starting value when x is 0.

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How do you identify a multiplicative relationship from a graph?

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A multiplicative relationship on a graph shows a curve that increases or decreases exponentially, rather than a straight line.

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What is a real-world example of an additive relationship?

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A real-world example of an additive relationship is saving money. If you save $10 every week, your total savings increases by $10 each week.