Understand linear functions

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. It may include curves, bends, or other shapes.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from its equation?

Back

A linear function will have no exponents greater than 1, no products of variables, and no variables in the denominator.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

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

Back

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

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

Is the function y = 2x + 3 linear or nonlinear?

Back

Linear

Tags

CCSS.8.F.A.3

Front

Is the function y = x^2 + 2 linear or nonlinear?

Back

Nonlinear

Tags

CCSS.8.F.A.3

Front

What is the general form of a linear equation?

Back

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

Front

What is the significance of the graph of a linear function?

Back

The graph of a linear function shows the relationship between the independent variable (x) and the dependent variable (y) in a visual format.

Tags

CCSS.HSF-IF.C.7A

Front

What are the characteristics of the graph of a linear function?

Back

The graph of a linear function is a straight line, has a constant slope, and can extend infinitely in both directions.

Tags

CCSS.HSF-IF.C.7A