Linear & Exponential Patterns

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What is a linear pattern?

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A linear pattern is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 4, 6, 8 is linear because each term increases by 2.

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CCSS.HSF.BF.A.2

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What is an exponential pattern?

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An exponential pattern is a sequence of numbers where each term is multiplied by a constant factor to get the next term. For example, 2, 4, 8, 16 is exponential because each term is multiplied by 2.

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CCSS.HSF.BF.A.2

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How do you identify a linear function from a set of values?

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A linear function can be identified if the differences between consecutive values are constant. For example, in the sequence 4, 12, 20, 28, 36, the differences are all 8.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is the formula for a linear function?

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The formula for a linear function is y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What does the slope of a linear function represent?

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The slope represents the rate of change of the function. It indicates how much y changes for a unit change in x.

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CCSS.8.EE.B.5

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What is the y-intercept in a linear function?

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The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

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How can you find the next term in a linear sequence?

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To find the next term in a linear sequence, add the common difference to the last term. For example, if the last term is 20 and the common difference is 8, the next term is 20 + 8 = 28.

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CCSS.HSF.BF.A.2

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What is a common difference in a linear sequence?

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The common difference is the constant amount that each term increases or decreases by in a linear sequence.

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CCSS.HSF.BF.A.2

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How do you determine the rule for an in-and-out table?

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To determine the rule for an in-and-out table, look for a consistent pattern in how the output changes with the input. For example, if the input increases by 1 and the output increases by 3, the rule is 'add 3'.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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What is the difference between linear and exponential growth?

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Linear growth increases by a constant amount, while exponential growth increases by a constant factor. Linear growth is steady, while exponential growth accelerates.