Linear/Nonlinear/Equations from tables

Front

What is a linear relationship in mathematics?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph, characterized by 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 when graphed, indicating that the rate of change is not constant.

Front

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

Back

A table represents a linear function if the differences between consecutive outputs (y-values) are constant for equal intervals of inputs (x-values).

Front

What is the general form of a linear equation?

Back

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

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 y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

What are some common forms of nonlinear equations?

Back

Common forms of nonlinear equations include quadratic equations (y = ax^2 + bx + c), exponential functions (y = a * b^x), and logarithmic functions (y = log_b(x)).

Front

How can you identify a nonlinear graph visually?

Back

A nonlinear graph can be identified by its curved shape, which indicates that the relationship between the variables is not constant.

Front

What is the significance of a function being linear or nonlinear in real-world applications?

Back

The significance lies in how predictions and relationships are modeled; linear functions are simpler and predict constant rates, while nonlinear functions can model more complex relationships.

Front

What is a scatter plot and how is it used to determine linearity?

Back

A scatter plot is a graph that displays values for two variables. It is used to visually assess the relationship between the variables and determine if it is linear or nonlinear.