linear and nonlinear equations

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 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 or any other shape that is not linear.

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 does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is the value of y when x = 0.

Front

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

Back

A function is linear if its graph is a straight line. If the graph curves or changes direction, the function is nonlinear.

Tags

CCSS.8.F.A.3

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2.

Tags

CCSS.8.F.A.3

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

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

Back

A linear equation represents a straight line, while a nonlinear equation represents a curve or any shape that is not straight.

Tags

CCSS.8.F.A.3