Linear vs Non-Linear

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, cubic, or exponential.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are the same, the function is linear.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

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What does the y-intercept represent in a linear function?

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

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What is the general form of a quadratic function?

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The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while quadratic functions have a variable rate of change and graph as parabolas.

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What is an example of a linear equation?

Back

An example of a linear equation is y = 3x + 2.

Tags

CCSS.8.F.A.3

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What is an example of a nonlinear equation?

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An example of a nonlinear equation is y = x^2 + 1.

Tags

CCSS.8.F.A.3

Front

How can you tell if a function is linear from its equation?

Back

If the equation can be rearranged to the form y = mx + b, it is linear. If it contains variables raised to powers greater than one or products of variables, it is nonlinear.

Tags

CCSS.8.F.A.3