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.

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).

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).

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.

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.

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.

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).

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.

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.