Rate of change from tables

Front

What is the rate of change in a linear relationship?

Back

The rate of change in a linear relationship is the constant amount by which the dependent variable changes for each unit change in the independent variable, often represented as the slope of the line.

Front

How do you calculate the rate of change from a table of values?

Back

To calculate the rate of change from a table of values, take the difference in the dependent variable (y-values) and divide it by the difference in the independent variable (x-values) for two points.

Front

What is 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.

Front

If the rate of change is negative, what does that indicate about the relationship between the variables?

Back

A negative rate of change indicates that as the independent variable increases, the dependent variable decreases, showing an inverse relationship.

Front

What does a rate of change of 0 indicate about a function?

Back

A rate of change of 0 indicates that the function is constant; the dependent variable does not change as the independent variable changes.

Front

What is the significance of a linear table in relation to rate of change?

Back

A linear table indicates that the rate of change is constant across the values, meaning the relationship between the variables can be represented by a straight line.

Front

How can you determine if a table represents a linear function?

Back

A table represents a linear function if the rate of change between any two points is the same.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a table has a rate of change of 5?

Back

A rate of change of 5 means that for every 1 unit increase in the independent variable, the dependent variable increases by 5 units.

Front

What is the relationship between slope and rate of change?

Back

The slope of a line is a numerical representation of the rate of change; it indicates how much the dependent variable changes for a unit change in the independent variable.