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

Front

How do you find the slope from two points?

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form 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 a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Tags

CCSS.8.EE.B.5

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the y-intercept in real-world scenarios?

Back

The y-intercept can represent the starting value of a situation in real-world applications, such as the initial cost before any changes.

Tags

CCSS.HSF.LE.B.5

Front

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

Back

If the differences between consecutive y-values are constant for equal differences in x-values, the function is linear.

Tags

CCSS.HSF-LE.A.1B

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.