Linear or NonLinear

Front

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

Front

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

Identify the characteristics of a linear equation.

Back

Linear equations have a constant rate of change, can be written in the form y = mx + b, and their graph is a straight line.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Identify the characteristics of a nonlinear equation.

Back

Nonlinear equations have a variable rate of change, cannot be expressed in the form y = mx + b, and their graph can be a curve or other shapes.

Tags

CCSS.8.F.A.3

Front

What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the function, indicating how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

Give an example of a linear function.

Back

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

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is y = x^2.

Tags

CCSS.8.F.A.3

Front

What is the general form of a quadratic function?

Back

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

Front

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

Back

If the graph is a straight line, the function is linear. If the graph is curved or has any bends, the function is nonlinear.

Tags

CCSS.8.F.A.3