Key Features 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 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

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How do you determine the x-intercept of a linear function?

Back

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

Front

What does a positive slope indicate about a linear function?

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 a negative slope indicate about a linear function?

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

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope is -3.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line represented by the equation y = 2x - 1?

Back

The slope is 2.

Tags

CCSS.8.EE.B.5

Front

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

Back

A zero slope indicates a horizontal line, meaning that y remains constant as x changes.

Tags

CCSS.8.EE.B.5