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 y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Tags

CCSS.8.EE.B.5

Front

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

Back

The y-intercept is found by setting x to 0 in the equation of the line and solving for y.

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, and A should be non-negative.

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

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

Back

A function is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Tags

CCSS.HSF-LE.A.1B

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line and calculating the rise (change in y) over the run (change in x).

Tags

CCSS.8.EE.B.5

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