Linear and Nonlinear 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. Examples include quadratic functions, exponential functions, and trigonometric functions.

Tags

CCSS.8.F.A.3

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope (m) of the line, which represents how much y changes for a unit change in x.

Tags

CCSS.HSF-LE.A.1B

Front

How do you identify a linear equation?

Back

A linear equation can be identified by its standard form, which is Ax + By = C, where A, B, and C are constants, and A and B are not both zero.

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.EE.B.6

CCSS.8.F.A.3

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if every input (x-value) has exactly one output (y-value). This can be tested using the vertical line test.

Front

What is the vertical line test?

Back

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

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the steepness of the line and the direction of the relationship between x and y. A positive slope means y increases as x increases, while a negative slope means y decreases as x increases.

Tags

CCSS.8.EE.B.5

Front

How can you find the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5