Linear vs Non-Linear

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

How can you determine if a function is linear or nonlinear from a table of values?

Back

If the ratio of the change in y to the change in x is constant for all intervals, the function is linear. If this ratio changes, the function is nonlinear.

Tags

CCSS.8.F.A.3

Front

What is the equation of a linear function?

Back

An example of a linear function is y = 8x, which represents a straight line with a slope of 8.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the equation of a nonlinear function?

Back

An example of a nonlinear function is y = 4x^2, which represents a parabola.

Tags

CCSS.8.F.A.3

Front

What does the slope of a linear function represent?

Back

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

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 line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

Is the function y = \frac{8}{x^2} linear or nonlinear?

Back

Nonlinear, because it does not form a straight line and the relationship between x and y is not constant.

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

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

Back

A linear equation is an equation that represents a straight line, while a linear function is a specific type of linear equation that defines a relationship between x and y.

Tags

CCSS.8.F.A.3