Linear and Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 graph to a straight line. Its rate of change is not constant.

Tags

CCSS.8.F.A.3

Front

What does the slope of a line represent?

Back

The slope of a line 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 is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

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

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean if a function has a constant slope?

Back

A function with a constant slope is linear, meaning the rate of change is the same throughout the entire function.

Tags

CCSS.HSF-LE.A.1B

Front

What is the rate of change in the equation y = 3x + 4?

Back

The rate of change is 3, which is the coefficient of x.

Tags

CCSS.HSF-LE.A.1B

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function will have a curve or bend in its graph, rather than being a straight line.

Tags

CCSS.8.F.A.3

Front

What is an example of a nonlinear equation?

Back

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

Tags

CCSS.8.F.A.3