Linear and Proportional 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. It has a constant rate of change.

Tags

CCSS.HSF-LE.A.1B

Front

What is a proportional relationship?

Back

A proportional relationship is a specific type of linear relationship where the ratio of the two variables is constant. It passes through the origin (0,0).

Tags

CCSS.7.RP.A.2D

Front

How do you find the rate of change in a linear relationship?

Back

The rate of change is found by dividing the change in the y-values by the change in the x-values (rise/run).

Tags

CCSS.HSF-LE.A.1B

Front

What does a constant slope indicate in a graph?

Back

A constant slope indicates a linear relationship, meaning the rate of change is the same throughout the graph.

Tags

CCSS.HSF-LE.A.1B

Front

What does a non-linear relationship look like on a graph?

Back

A non-linear relationship does not form a straight line and has a varying rate of change.

Tags

CCSS.8.F.A.3

Front

If a line has a slope of 2, what does that mean?

Back

A slope of 2 means that for every 1 unit increase in x, the y-value increases by 2 units.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a line that goes through the points (1, 3) and (2, 7)?

Back

The slope is 4, calculated as (7-3)/(2-1).

Tags

CCSS.8.EE.B.5

Front

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

Back

The 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

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).

Front

How can you tell if a relationship is proportional from a table of values?

Back

If the ratios of y to x are constant for all pairs of values, the relationship is proportional.

Tags

CCSS.7.RP.A.2A