8th Grade Linear Functions

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 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 dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

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) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

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 y = mx + b.

Front

What is the constant of proportionality in a linear relationship?

Back

The constant of proportionality is the slope of the line when the relationship is directly proportional, indicating how much y changes for a unit change in x.

Tags

CCSS.HSF-LE.A.1B

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, showing an inverse relationship between the two variables.

Tags

CCSS.8.EE.B.5

Front

How can you identify the slope from the equation of a line in slope-intercept form?

Back

In the slope-intercept form y = mx + b, the slope is the coefficient of x (m).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does it mean if a line has a slope of zero?

Back

A slope of zero means the line is horizontal, indicating that the value of y remains constant regardless of the value of x.

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 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 find the y-intercept from a linear equation?

Back

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