Characteristics of Linear 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 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 y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

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. It is represented as (0, b) in the equation y = mx + b.

Front

What is the x-intercept of a linear function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis. It is represented as (a, 0) where a is the value of x when y = 0.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, often expressed as (-∞, ∞).

Front

What is the range of a linear function?

Back

The range of a linear function is also all real numbers, often expressed as (-∞, ∞).

Front

What does it mean if a linear function has a positive slope?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Tags

CCSS.8.EE.B.5

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Tags

CCSS.8.EE.B.5