Different Representations of Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph, typically described by the equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.HSF-LE.A.1B

Front

What does the slope of a line represent in a linear relationship?

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 much y changes for a unit change in x.

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. It is the value of y when x is 0, represented by the term 'b' in the equation y = mx + b.

Front

How can you determine which of two linear equations has a steeper slope?

Back

You can determine which equation has a steeper slope by comparing the absolute values of their slopes (m). The equation with the larger absolute value of m has a steeper slope.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, showing an inverse relationship.

Tags

CCSS.8.EE.B.5

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases, showing a direct relationship.

Tags

CCSS.8.EE.B.5

Front

How can you find the rate of change from a graph?

Back

The rate of change can be found by calculating the slope of the line on the graph, which is determined by the formula (change in y) / (change in x).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

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

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means that the line is horizontal, indicating that there is no change in the dependent variable (y) as the independent variable (x) changes.

Tags

CCSS.8.EE.B.5

Front

What is the significance of the steepness of a line in a graph?

Back

The steepness of a line in a graph indicates the rate of change; steeper lines represent greater rates of change, while flatter lines represent smaller rates of change.

Tags

CCSS.8.EE.B.5