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 line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is.

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. In the equation y = mx + b, b represents the y-intercept.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) has exactly one output (y-value). If any x-value is repeated with different y-values, it is not a function.

Tags

CCSS.8.F.A.1

Front

What does a positive slope indicate about a linear function?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does a negative slope indicate about a linear function?

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the difference between a function and a non-function?

Back

A function has a unique output for each input, while a non-function has at least one input that corresponds to multiple outputs.

Tags

CCSS.8.F.A.1

Front

In the equation y = mx + b, what does 'm' represent?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

In the equation y = mx + b, what does 'b' represent?

Back

In the equation y = mx + b, 'b' represents the y-intercept of the line.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between inputs and outputs, showing how each input is paired with an output.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1