A.3(B) calculate the rate of change of a linear function

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = 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 rate of change represent in a linear function?

Back

The rate of change in a linear function represents how much the output (y) changes for a unit change in the input (x). It is equivalent to the slope (m) of the line.

Tags

CCSS.HSF-LE.A.1B

Front

How do you calculate the slope of a linear function?

Back

The slope (m) of a linear function 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 slope of the line that passes through the points (2, 3) and (4, 7)?

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

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 by the value of b in the equation f(x) = mx + b.

Front

If a linear function has a slope of 0, what does that indicate about the function?

Back

A slope of 0 indicates that the function is a horizontal line, meaning that the output (y) does not change regardless of the input (x).

Tags

CCSS.8.EE.B.5

Front

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

Back

A negative slope indicates that as the input (x) increases, the output (y) decreases, resulting in a downward slant of the line.

Tags

CCSS.8.EE.B.5

Front

How can you determine if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope (m) is positive and decreasing if the slope (m) is negative.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

The slope-intercept form of a line is given by the equation 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 it mean for two linear functions to be parallel?

Back

Two linear functions are parallel if they have the same slope (m) but different y-intercepts (b). They will never intersect.

Tags

CCSS.8.EE.B.5