Non and Linear Lines

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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 f(x) = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its graph can be a curve, a circle, or any other shape that is not a straight line.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear equation from its graph?

Back

A linear equation can be identified by its graph being a straight line, which has a constant slope.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the general form of a linear equation in two variables?

Back

The general form of a linear equation in two variables is Ax + By = C, where A, B, and C are constants.

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What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable with respect to the independent variable. It indicates how steep the line is.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the line crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.

Front

What are some examples of nonlinear functions?

Back

Examples of nonlinear functions include quadratic functions (e.g., f(x) = x^2), exponential functions (e.g., f(x) = e^x), and trigonometric functions (e.g., f(x) = sin(x)).

Tags

CCSS.8.F.A.3

Front

What is the difference between linear and nonlinear graphs?

Back

Linear graphs are straight lines with a constant slope, while nonlinear graphs can be curves or other shapes that do not have a constant slope.

Tags

CCSS.8.F.A.3

Front

How can you determine if a function is linear or nonlinear from its equation?

Back

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

Tags

CCSS.8.F.A.3

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input variable.

Tags

CCSS.HSF-IF.C.7B