Linear vs. Nonlinear Tables and Graphs

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, indicating a constant rate of change.

Front

What is a nonlinear relationship?

Back

A nonlinear relationship is a relationship between two variables that does not form a straight line on a graph, indicating a variable rate of change.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in the y-values for equal intervals of x-values.

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).

Front

What is the formula for the slope of a line?

Back

The formula for the slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does it mean if a function has a constant rate of change?

Back

It means that for every unit increase in the independent variable (x), the dependent variable (y) increases by a fixed amount.

Front

How can you tell if a graph is nonlinear?

Back

A graph is nonlinear if it curves or has bends, indicating that the rate of change is not constant.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which forms a parabola on a graph.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent speed, cost per item, or any rate of change in real-world scenarios.