Linear or Nonlinear

Front

What is a linear equation?

Back

A linear equation is an equation that can be expressed in the form y = mx + b, where m and b are constants, and the graph of the equation is a straight line.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a nonlinear equation?

Back

A nonlinear equation is an equation that does not form a straight line when graphed. It can include terms such as x^2, x^3, or other non-linear functions.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from its equation?

Back

A linear function can be identified by the highest power of the variable being 1, and it can be written in the form y = mx + b.

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 = 0, where A, B, and C are constants.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Tags

CCSS.8.EE.B.5

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a nonlinear function has a variable rate of change and graphs as a curve.

Tags

CCSS.8.F.A.3

Front

Can a linear function have a quadratic term?

Back

No, a linear function cannot have a quadratic term (e.g., x^2) as it would make the function nonlinear.

Tags

CCSS.8.F.A.3

Front

What is a common example of a nonlinear function?

Back

A common example of a nonlinear function is a quadratic function, such as y = ax^2 + bx + c.

Front

How can you determine if a function represented by a table is linear?

Back

To determine if a function represented by a table is linear, check if the differences between consecutive y-values are constant for equal intervals of x.

Tags

CCSS.HSF-LE.A.1B