Key Features of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, defined by the equation 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

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

Back

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

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the coordinates (0, b) in the equation y = mx + b.

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 a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in y as x changes.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would require division by zero when calculating slope.

Tags

CCSS.8.EE.B.5

Front

How do you calculate the slope between 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 significance of the point (0, b) in a linear function?

Back

The point (0, b) is the y-intercept, indicating where the line crosses the y-axis.

Tags

CCSS.HSF-IF.C.7A